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The only given values are the sum of an infinite geometric series which is equal to 9/2, and the second term which is equal to -2. How do I find the common ratio here?

sup
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    If the first term is $a_1$ and the common ratio is $r$, then the second term is $a_2 = a_1r$ and the sum is $\frac{a_1}{1-r} = \frac{a_2}{r(1-r)}$. Use this to solve for $r$. – Brian Tung Nov 25 '20 at 07:53

2 Answers2

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Assume the geometric sequence to be

$$a,ar,ar^2...$$

(where $r$ is the common ratio)

Given that $ar=-2$ and $\frac{a}{1-r}=\frac92$

Two equations and two variables. I bet you can solve it now.

DatBoi
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Here is a neater version. From the formula:

$$a = \frac{9}{2}(1-r)$$ $$ar = -2= \frac{9}{2}(1-r)r$$

and remember that $|r| < 1$ for the series to converge.

Toby Mak
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