Find the n th partial sum of the geometric sequence. $1,-4,16,-64,256, \ldots, \quad n=7$
A)3326
B)3277
C)-819
D)3620
E)-51

Question

Quizplus · Accepted Answer

The given sequence is a geometric sequence with the first term $a = 1$ and common ratio $r = -4$. The nth partial sum of a geometric sequence is given by the formula $S_n = \frac{a(1 - r^n)}{1 - r}$ when $r \neq 1$. Substituting $a = 1$, $r = -4$, and $n = 7$, we get $S_7 = \frac{1(1 - (-4)^7)}{1 - (-4)} = \frac{1 - (-16384)}{5} = \frac{16385}{5} = 3277$.

Find the N Th Partial Sum of the Geometric Sequence 1,−4,16,−64,256,…,n=71,-4,16,-64,256, \ldots, \quad n=71,−4,16,−64,256,…,n=7

Find the N Th Partial Sum of the Geometric Sequence $1,-4,16,-64,256, \ldots, \quad n=7$