Can someone help The Next CEO of Stack OverflowIf $(c_n)_n$ is the sum of geometric and arithmetic sequences. How to get the original sequences back?Given common terms (and their position) between an arithmetic and geometric sequences, find the common ratio.Series - calculating the sumFirst term of a series with two zeros and a constant second differenceGiven a sequence find nth termFinding which term in a sequence the last term of a sum corresponds to.Consecutive termsWrite the first ten terms of the arithmetic sequence given the first term and some other informationFind three numbers that can be consecutive terms of geometric sequence and first, second and seventh term of arithmetic sequence and whose sum is $93$sequence with first difference and second constant ratio in first difference

What happened in Rome, when the western empire "fell"?

How do I avoid eval and parse?

Why don't programming languages automatically manage the synchronous/asynchronous problem?

Why do we use the plural of movies in this phrase "We went to the movies last night."?

Should I tutor a student who I know has cheated on their homework?

Can someone help

How do I transpose the 1st and -1th levels of an arbitrarily nested array?

Interfacing a button to MCU (and PC) with 50m long cable

How did the Bene Gesserit know how to make a Kwisatz Haderach?

What does "Its cash flow is deeply negative" mean?

MessageLevel in QGIS3

Why has the US not been more assertive in confronting Russia in recent years?

Elegant way to replace substring in a regex with optional groups in Python?

What connection does MS Office have to Netscape Navigator?

Is it my responsibility to learn a new technology in my own time my employer wants to implement?

Why is the US ranked as #45 in Press Freedom ratings, despite its extremely permissive free speech laws?

Is "for causing autism in X" grammatical?

What is the result of assigning to std::vector<T>::begin()?

How do we know the LHC results are robust?

How did people program for Consoles with multiple CPUs?

Is there an analogue of projective spaces for proper schemes?

Why do remote companies require working in the US?

Would this house-rule that treats advantage as a +1 to the roll instead (and disadvantage as -1) and allows them to stack be balanced?

Bold, vivid family



Can someone help



The Next CEO of Stack OverflowIf $(c_n)_n$ is the sum of geometric and arithmetic sequences. How to get the original sequences back?Given common terms (and their position) between an arithmetic and geometric sequences, find the common ratio.Series - calculating the sumFirst term of a series with two zeros and a constant second differenceGiven a sequence find nth termFinding which term in a sequence the last term of a sum corresponds to.Consecutive termsWrite the first ten terms of the arithmetic sequence given the first term and some other informationFind three numbers that can be consecutive terms of geometric sequence and first, second and seventh term of arithmetic sequence and whose sum is $93$sequence with first difference and second constant ratio in first difference










2












$begingroup$


Consider the geometric sequence $1, a, a^2, a^3,dots$ Suppose that the sum of two consecutive terms in the sequence gives the next term in the sequence. Find $a$.










share|cite|improve this question









New contributor




lollol is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$







  • 8




    $begingroup$
    So $1+a = a^2$ (make sure you know why!). Can you find $a$ from this?
    $endgroup$
    – Minus One-Twelfth
    2 hours ago







  • 1




    $begingroup$
    Son of Bonacci would know the answer right away.
    $endgroup$
    – dnqxt
    2 hours ago















2












$begingroup$


Consider the geometric sequence $1, a, a^2, a^3,dots$ Suppose that the sum of two consecutive terms in the sequence gives the next term in the sequence. Find $a$.










share|cite|improve this question









New contributor




lollol is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$







  • 8




    $begingroup$
    So $1+a = a^2$ (make sure you know why!). Can you find $a$ from this?
    $endgroup$
    – Minus One-Twelfth
    2 hours ago







  • 1




    $begingroup$
    Son of Bonacci would know the answer right away.
    $endgroup$
    – dnqxt
    2 hours ago













2












2








2


2



$begingroup$


Consider the geometric sequence $1, a, a^2, a^3,dots$ Suppose that the sum of two consecutive terms in the sequence gives the next term in the sequence. Find $a$.










share|cite|improve this question









New contributor




lollol is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$




Consider the geometric sequence $1, a, a^2, a^3,dots$ Suppose that the sum of two consecutive terms in the sequence gives the next term in the sequence. Find $a$.







sequences-and-series






share|cite|improve this question









New contributor




lollol is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question









New contributor




lollol is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|cite|improve this question




share|cite|improve this question








edited 2 hours ago









Lehs

7,07931664




7,07931664






New contributor




lollol is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked 2 hours ago









lollollollol

221




221




New contributor




lollol is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





lollol is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






lollol is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







  • 8




    $begingroup$
    So $1+a = a^2$ (make sure you know why!). Can you find $a$ from this?
    $endgroup$
    – Minus One-Twelfth
    2 hours ago







  • 1




    $begingroup$
    Son of Bonacci would know the answer right away.
    $endgroup$
    – dnqxt
    2 hours ago












  • 8




    $begingroup$
    So $1+a = a^2$ (make sure you know why!). Can you find $a$ from this?
    $endgroup$
    – Minus One-Twelfth
    2 hours ago







  • 1




    $begingroup$
    Son of Bonacci would know the answer right away.
    $endgroup$
    – dnqxt
    2 hours ago







8




8




$begingroup$
So $1+a = a^2$ (make sure you know why!). Can you find $a$ from this?
$endgroup$
– Minus One-Twelfth
2 hours ago





$begingroup$
So $1+a = a^2$ (make sure you know why!). Can you find $a$ from this?
$endgroup$
– Minus One-Twelfth
2 hours ago





1




1




$begingroup$
Son of Bonacci would know the answer right away.
$endgroup$
– dnqxt
2 hours ago




$begingroup$
Son of Bonacci would know the answer right away.
$endgroup$
– dnqxt
2 hours ago










2 Answers
2






active

oldest

votes


















3












$begingroup$

$a^n + a^n + 1 = a^n + 2; tag 1$



$a ne 0 Longrightarrow 1 + a = a^2 Longrightarrow a^2 - a - 1 = 0; tag 2$



$a_pm = dfrac1 pm sqrt(-1)^2 - 4(1)(-1)2 = dfrac1 pm sqrt 52; tag 3$



note that



$a_+ a_- = -1; ; a_+ + a_- = 1. tag 4$






share|cite|improve this answer









$endgroup$








  • 1




    $begingroup$
    In fact, $a=0$ is also a solution.
    $endgroup$
    – Ross Millikan
    1 hour ago










  • $begingroup$
    @RossMillikan: except when we start at the beginning: $1 + 0 = 1 ne 0$!
    $endgroup$
    – Robert Lewis
    1 hour ago






  • 1




    $begingroup$
    I read the question to have one set of three consecutive terms to satisfy the requirement, so the second, third, and fourth of $1,0,0,0,0,ldots$ do. I agree it is not clear and you might require that every set of three terms does.
    $endgroup$
    – Ross Millikan
    1 hour ago











  • $begingroup$
    @RossMillikan: yes, I see your point!
    $endgroup$
    – Robert Lewis
    1 hour ago


















3












$begingroup$

$$1+a = a^2$$
$$textBy Quadratic formula, you get a = frac 1 pm sqrt52$$
You check that it works throughout the equation... as $a+a^2 = a^3$ and so on.. but you will find that $a^2 - a -1$ is always a factor of all equation.



Hence $a = frac 1 pm sqrt52$






share|cite|improve this answer









$endgroup$








  • 1




    $begingroup$
    The question asks if any set of three terms satisfies the requirement. If $a_n$ is the first one, you can divide by $a_n$ to get your equation, but that should be noted.
    $endgroup$
    – Ross Millikan
    1 hour ago











Your Answer





StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);






lollol is a new contributor. Be nice, and check out our Code of Conduct.









draft saved

draft discarded


















StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3167818%2fcan-someone-help%23new-answer', 'question_page');

);

Post as a guest















Required, but never shown

























2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






active

oldest

votes









3












$begingroup$

$a^n + a^n + 1 = a^n + 2; tag 1$



$a ne 0 Longrightarrow 1 + a = a^2 Longrightarrow a^2 - a - 1 = 0; tag 2$



$a_pm = dfrac1 pm sqrt(-1)^2 - 4(1)(-1)2 = dfrac1 pm sqrt 52; tag 3$



note that



$a_+ a_- = -1; ; a_+ + a_- = 1. tag 4$






share|cite|improve this answer









$endgroup$








  • 1




    $begingroup$
    In fact, $a=0$ is also a solution.
    $endgroup$
    – Ross Millikan
    1 hour ago










  • $begingroup$
    @RossMillikan: except when we start at the beginning: $1 + 0 = 1 ne 0$!
    $endgroup$
    – Robert Lewis
    1 hour ago






  • 1




    $begingroup$
    I read the question to have one set of three consecutive terms to satisfy the requirement, so the second, third, and fourth of $1,0,0,0,0,ldots$ do. I agree it is not clear and you might require that every set of three terms does.
    $endgroup$
    – Ross Millikan
    1 hour ago











  • $begingroup$
    @RossMillikan: yes, I see your point!
    $endgroup$
    – Robert Lewis
    1 hour ago















3












$begingroup$

$a^n + a^n + 1 = a^n + 2; tag 1$



$a ne 0 Longrightarrow 1 + a = a^2 Longrightarrow a^2 - a - 1 = 0; tag 2$



$a_pm = dfrac1 pm sqrt(-1)^2 - 4(1)(-1)2 = dfrac1 pm sqrt 52; tag 3$



note that



$a_+ a_- = -1; ; a_+ + a_- = 1. tag 4$






share|cite|improve this answer









$endgroup$








  • 1




    $begingroup$
    In fact, $a=0$ is also a solution.
    $endgroup$
    – Ross Millikan
    1 hour ago










  • $begingroup$
    @RossMillikan: except when we start at the beginning: $1 + 0 = 1 ne 0$!
    $endgroup$
    – Robert Lewis
    1 hour ago






  • 1




    $begingroup$
    I read the question to have one set of three consecutive terms to satisfy the requirement, so the second, third, and fourth of $1,0,0,0,0,ldots$ do. I agree it is not clear and you might require that every set of three terms does.
    $endgroup$
    – Ross Millikan
    1 hour ago











  • $begingroup$
    @RossMillikan: yes, I see your point!
    $endgroup$
    – Robert Lewis
    1 hour ago













3












3








3





$begingroup$

$a^n + a^n + 1 = a^n + 2; tag 1$



$a ne 0 Longrightarrow 1 + a = a^2 Longrightarrow a^2 - a - 1 = 0; tag 2$



$a_pm = dfrac1 pm sqrt(-1)^2 - 4(1)(-1)2 = dfrac1 pm sqrt 52; tag 3$



note that



$a_+ a_- = -1; ; a_+ + a_- = 1. tag 4$






share|cite|improve this answer









$endgroup$



$a^n + a^n + 1 = a^n + 2; tag 1$



$a ne 0 Longrightarrow 1 + a = a^2 Longrightarrow a^2 - a - 1 = 0; tag 2$



$a_pm = dfrac1 pm sqrt(-1)^2 - 4(1)(-1)2 = dfrac1 pm sqrt 52; tag 3$



note that



$a_+ a_- = -1; ; a_+ + a_- = 1. tag 4$







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered 1 hour ago









Robert LewisRobert Lewis

48.5k23167




48.5k23167







  • 1




    $begingroup$
    In fact, $a=0$ is also a solution.
    $endgroup$
    – Ross Millikan
    1 hour ago










  • $begingroup$
    @RossMillikan: except when we start at the beginning: $1 + 0 = 1 ne 0$!
    $endgroup$
    – Robert Lewis
    1 hour ago






  • 1




    $begingroup$
    I read the question to have one set of three consecutive terms to satisfy the requirement, so the second, third, and fourth of $1,0,0,0,0,ldots$ do. I agree it is not clear and you might require that every set of three terms does.
    $endgroup$
    – Ross Millikan
    1 hour ago











  • $begingroup$
    @RossMillikan: yes, I see your point!
    $endgroup$
    – Robert Lewis
    1 hour ago












  • 1




    $begingroup$
    In fact, $a=0$ is also a solution.
    $endgroup$
    – Ross Millikan
    1 hour ago










  • $begingroup$
    @RossMillikan: except when we start at the beginning: $1 + 0 = 1 ne 0$!
    $endgroup$
    – Robert Lewis
    1 hour ago






  • 1




    $begingroup$
    I read the question to have one set of three consecutive terms to satisfy the requirement, so the second, third, and fourth of $1,0,0,0,0,ldots$ do. I agree it is not clear and you might require that every set of three terms does.
    $endgroup$
    – Ross Millikan
    1 hour ago











  • $begingroup$
    @RossMillikan: yes, I see your point!
    $endgroup$
    – Robert Lewis
    1 hour ago







1




1




$begingroup$
In fact, $a=0$ is also a solution.
$endgroup$
– Ross Millikan
1 hour ago




$begingroup$
In fact, $a=0$ is also a solution.
$endgroup$
– Ross Millikan
1 hour ago












$begingroup$
@RossMillikan: except when we start at the beginning: $1 + 0 = 1 ne 0$!
$endgroup$
– Robert Lewis
1 hour ago




$begingroup$
@RossMillikan: except when we start at the beginning: $1 + 0 = 1 ne 0$!
$endgroup$
– Robert Lewis
1 hour ago




1




1




$begingroup$
I read the question to have one set of three consecutive terms to satisfy the requirement, so the second, third, and fourth of $1,0,0,0,0,ldots$ do. I agree it is not clear and you might require that every set of three terms does.
$endgroup$
– Ross Millikan
1 hour ago





$begingroup$
I read the question to have one set of three consecutive terms to satisfy the requirement, so the second, third, and fourth of $1,0,0,0,0,ldots$ do. I agree it is not clear and you might require that every set of three terms does.
$endgroup$
– Ross Millikan
1 hour ago













$begingroup$
@RossMillikan: yes, I see your point!
$endgroup$
– Robert Lewis
1 hour ago




$begingroup$
@RossMillikan: yes, I see your point!
$endgroup$
– Robert Lewis
1 hour ago











3












$begingroup$

$$1+a = a^2$$
$$textBy Quadratic formula, you get a = frac 1 pm sqrt52$$
You check that it works throughout the equation... as $a+a^2 = a^3$ and so on.. but you will find that $a^2 - a -1$ is always a factor of all equation.



Hence $a = frac 1 pm sqrt52$






share|cite|improve this answer









$endgroup$








  • 1




    $begingroup$
    The question asks if any set of three terms satisfies the requirement. If $a_n$ is the first one, you can divide by $a_n$ to get your equation, but that should be noted.
    $endgroup$
    – Ross Millikan
    1 hour ago















3












$begingroup$

$$1+a = a^2$$
$$textBy Quadratic formula, you get a = frac 1 pm sqrt52$$
You check that it works throughout the equation... as $a+a^2 = a^3$ and so on.. but you will find that $a^2 - a -1$ is always a factor of all equation.



Hence $a = frac 1 pm sqrt52$






share|cite|improve this answer









$endgroup$








  • 1




    $begingroup$
    The question asks if any set of three terms satisfies the requirement. If $a_n$ is the first one, you can divide by $a_n$ to get your equation, but that should be noted.
    $endgroup$
    – Ross Millikan
    1 hour ago













3












3








3





$begingroup$

$$1+a = a^2$$
$$textBy Quadratic formula, you get a = frac 1 pm sqrt52$$
You check that it works throughout the equation... as $a+a^2 = a^3$ and so on.. but you will find that $a^2 - a -1$ is always a factor of all equation.



Hence $a = frac 1 pm sqrt52$






share|cite|improve this answer









$endgroup$



$$1+a = a^2$$
$$textBy Quadratic formula, you get a = frac 1 pm sqrt52$$
You check that it works throughout the equation... as $a+a^2 = a^3$ and so on.. but you will find that $a^2 - a -1$ is always a factor of all equation.



Hence $a = frac 1 pm sqrt52$







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered 1 hour ago









rashrash

595116




595116







  • 1




    $begingroup$
    The question asks if any set of three terms satisfies the requirement. If $a_n$ is the first one, you can divide by $a_n$ to get your equation, but that should be noted.
    $endgroup$
    – Ross Millikan
    1 hour ago












  • 1




    $begingroup$
    The question asks if any set of three terms satisfies the requirement. If $a_n$ is the first one, you can divide by $a_n$ to get your equation, but that should be noted.
    $endgroup$
    – Ross Millikan
    1 hour ago







1




1




$begingroup$
The question asks if any set of three terms satisfies the requirement. If $a_n$ is the first one, you can divide by $a_n$ to get your equation, but that should be noted.
$endgroup$
– Ross Millikan
1 hour ago




$begingroup$
The question asks if any set of three terms satisfies the requirement. If $a_n$ is the first one, you can divide by $a_n$ to get your equation, but that should be noted.
$endgroup$
– Ross Millikan
1 hour ago










lollol is a new contributor. Be nice, and check out our Code of Conduct.









draft saved

draft discarded


















lollol is a new contributor. Be nice, and check out our Code of Conduct.












lollol is a new contributor. Be nice, and check out our Code of Conduct.











lollol is a new contributor. Be nice, and check out our Code of Conduct.














Thanks for contributing an answer to Mathematics Stack Exchange!


  • Please be sure to answer the question. Provide details and share your research!

But avoid


  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.

Use MathJax to format equations. MathJax reference.


To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3167818%2fcan-someone-help%23new-answer', 'question_page');

);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







Popular posts from this blog

名間水力發電廠 目录 沿革 設施 鄰近設施 註釋 外部連結 导航菜单23°50′10″N 120°42′41″E / 23.83611°N 120.71139°E / 23.83611; 120.7113923°50′10″N 120°42′41″E / 23.83611°N 120.71139°E / 23.83611; 120.71139計畫概要原始内容臺灣第一座BOT 模式開發的水力發電廠-名間水力電廠名間水力發電廠 水利署首件BOT案原始内容《小檔案》名間電廠 首座BOT水力發電廠原始内容名間電廠BOT - 經濟部水利署中區水資源局

Prove that NP is closed under karp reduction?Space(n) not closed under Karp reductions - what about NTime(n)?Class P is closed under rotation?Prove or disprove that $NL$ is closed under polynomial many-one reductions$mathbfNC_2$ is closed under log-space reductionOn Karp reductionwhen can I know if a class (complexity) is closed under reduction (cook/karp)Check if class $PSPACE$ is closed under polyonomially space reductionIs NPSPACE also closed under polynomial-time reduction and under log-space reduction?Prove PSPACE is closed under complement?Prove PSPACE is closed under union?

Is my guitar’s action too high? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Strings too stiff on a recently purchased acoustic guitar | Cort AD880CEIs the action of my guitar really high?Μy little finger is too weak to play guitarWith guitar, how long should I give my fingers to strengthen / callous?When playing a fret the guitar sounds mutedPlaying (Barre) chords up the guitar neckI think my guitar strings are wound too tight and I can't play barre chordsF barre chord on an SG guitarHow to find to the right strings of a barre chord by feel?High action on higher fret on my steel acoustic guitar