How do you find $S_n$ for the geometric series $a_1=80$ , r=-1/2, n=7?

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Answer 1 · 2018-02-02T13:58:34

$53.75$

Just use the formula for finding the sum of $n$ terms while the common ratio.

$S_n = (a(1 - r^n))/(1-r)$

Substituting the values,

$S_n = (80(1 - (-1/2)^7))/(1 - (-1/2)) = (80 * (1 + 1/128))/(1 + 1/2) = (80 * 129/128)/(3/2) = (80.625)/(1.5) = 53.75$

It makes sense that The sum is actually less than the first term of the Geometric Progression, As $r = -1/2 < 1$

How do you find S_nS_n for the geometric series a_1=80a_1=80, r=-1/2, n=7?