(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the first three terms of a geometric sequence given that the sum of the first four terms is 65/3 and the sum to infinity is 27.

2. Relevant equations

[tex]

\begin{array}{1}

S_n = \frac{a(1 - r^n)}{1 - r}\\

S_n = \frac{a(r^n - 1}{r - 1}

\end{array}

[/tex]

3. The attempt at a solution

I'm trying to get two equations in two unknowns.

I end with

a + 27r = 27

But I get lost after that. Trying to solve the sum leaves me with a equation to fourth or fifth power which I can't solve.

I'm sure there's a simple approach to this.

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# Find the first three terms a geometric sequence

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