How do you find the number of terms given $s_n=820$ and $1+9+81+729+...$ ?

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Answer 1 · 2016-08-23T02:10:04

$n = 4$

We use the formula $s_n = (a(1 - r^n))/(1 - r)$ to find the sum of any geometric series.

In our case, $r = 9$ , $a = 1$ and $s_n = 820$ . We are looking for $n$ .

$820 = (1(1 - 9^n))/(1 - 9)$

$820(-8) = 1 - 9^n$

$-6560 - 1 = -9^n$

$-6561 = -9^n$

$6561 = 9^n$

$9^4 = 9^n$

$n = 4$

Hence, there are $4$ terms in this series.

How do you find the number of terms given s_n=820s_n=820 and 1+9+81+729+...1+9+81+729+...?