How do you find $a_{1}$ $a_1$ for the geometric series given $S_{n} = - 364$ $S_n=-364$ , r=-3, n=6?

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Answer 1 · 2016-10-22T15:49:57

$a_{1} = 2$ $a_1 = 2$

We use the formula $s_{n} = \frac{a (1 - r^{n})}{1 - r}$ $s_n = (a(1 - r^n))/(1 - r)$ to find the sum of a geometric series.

$- 364 = \frac{a (1 - {(- 3)}^{6})}{1 - (- 3)}$ $-364 = (a(1 - (-3)^6))/(1 - (-3))$

$- 364 = \frac{a (- 728)}{4}$ $-364 = (a(-728))/(4)$

$- 364 = - 182 a$ $-364 = -182a$

$a = 2$ $a = 2$

Hopefully this helps!

How do you find a1a_1 for the geometric series given Sn=−364S_n=-364, r=-3, n=6?