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Questions tagged [geometric-series]

For questions about or involving geometric series, a series where successive terms have a common ratio.

A geometric series is of the form

$$\sum_{n=0}^{\infty}ar^n.$$

If $|r| < 1$, then the series converges to $\frac{a}{1-r}$. If $|r| \geq 1$, the series diverges.

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Simplify a finite series

can someone help me simplify the following formula? $$y =…
d_air
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Can a geometric sequence go on forever?

I have a geometric sequence whose n-th term is $11^n$: $1,11,121,1331,...$ I want to know if the pattern continues forever. I understand that if I sum these numbers up, my common ratio is 11 which is not between -1 and 1 so the sum doesn't converge…
user130306
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Explanation for visual representation of geometric series

I found these on the Art of Problem Solving website here. I just don't see how the first image would give you $\frac{1}{3}+\frac{1}{3^2}+...$ and I'm unable to see how the second one is divided into fourths. Normally for these problems, I can look…
user130306
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comparing area of a square with area of rectangle

If we have a geometric sequence we have $a_1, a_1*r, a_2*r$ So $b=a_1*r$ and $c=a_2*r$ The square has area $b^2$ which is $(a_1*r)^2$ and the rectangle has area $ac = a_1*a_2*r$ I don't know which one is bigger or if this was even a correct way…
user130306
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How do I find the common ratio of a geometric sequence?

A geometric sequence has its first term equal to $12$ and its fourth term equal to $-96$. How do I find the common ratio? And find the sum of the first $14$ terms
Outsider
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Convert expression to standard geometric progression

How can I transform a formula describing a curve (a discrete series) to the standard formula for a geometric progression? (Note: Maths is still very much a foreign language to me. I could be using any of these terms incorrectly. I could be using…
bignose
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Finding the infinite sum of a geometric series

I have the series: $3 + \frac{3}{2} + \frac{3}{4} + \frac{3}{8}$, I need to calculate the exact value of it. I have found that the equation of this is $a_n = 3(\frac{1}{2})^{n-1}$, but I am not sure how to progress from here. Would guess that I…
Big Papa
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Find the Year of the Question paper it belongs to (Maths 9709 )

The first two terms of a geometric progression are where 0<θ<π/2 (i) Find the set of values of θ for which the progression is convergent. [2] Which Year Question paper is this? Year with variant Please Pic of the Qn
Mastermind-7
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Me possibly overthinking a geometric series question

I am creating a study sheet for geometric series and came across this questions Do you think there is an infinite geometric series with first term 10 and a sum of 4? If so, find one infinite geometric series with first term 10 and a sum of 4, as…
K Math
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Geometric series, TMUA exam question, please help!

Q. A geometric series has first term $4$ and common ratio $r$. Where $0 < r < 1$ The first, second and fourth terms of this geometric series form three successive terms of an arithmetic series. The sum of infinity of the geometric series is. A. …
Kathryn Stiff-Tompkins
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A geometric series has second term $6$ and ratio of the seventh term to the sixth term is $3$. What does this question really means?

A geometric series has second term 6 and ratio of the seventh term to the sixth term is $3$. What does this question really means? Sorry I just couldn't get this question. $t(2)=6,$ $6=ar$ from my interpretation is the question saying $t(7) : t(6)…
Jon Wick
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Calculate total length of linear growth equation

Alright, I'm having a really difficult time putting the correct mathematical terms on the problem I'm trying to deal with (which is probably why I can't find an answer), so bear with me.* 0 |--> *----*----*-------*------------* | | | …
James Wright
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Find the indicated term of the geometric sequence algebraically.

a1=18, r=4/3, 8th term 1.Find the indicated term of the geometric sequence algebraically.
Lala
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Is this in the form of a geometric series?

Is the equation below a geometric series? I think yes but the only thing that bothers me is the $1+$ in the numerator. I think it would usually be $1-$.
Rory McEwan
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Find the numerical value of the first 3 terms of a geometric sequence

The first 3 terms in a geometric sequence are $x, x+5, x+9$. With this information, determine the numerical value of these terms. We didn't go over this in class. I'm not sure what formula to use. $a=x$ $r=?$ Any help is greatly appreciated.
Grimestock
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