Find a general term a n for the geometric sequence.
-$$8 , - 4,2 , - 1 , \frac { 1 } { 2 } ,$$
A) $a _ { n } = \frac { 1 } { 8 } ( - 2 ) n - 1$
B) $a _ { n } = 6 \left( - \frac { 1 } { 4 } \right) ^ { n - 1 }$
C) $a _ { n } = 8 \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$
D) $a _ { n } = 8 \left( - \frac { 1 } { 2 } \right) ^ { n - 1 }$

Question

Quizplus · Accepted Answer

The sequence alternates in sign, which suggests a negative ratio. The absolute value of the ratio between consecutive terms is $\frac{1}{2}$, so the common ratio is $-\frac{1}{2}$. The first term is 8, so the general term is $a_n = 8(-\frac{1}{2})^{n-1}$.

Find a General Term An for the Geometric Sequence 8,−4,2,−1,12,8 , - 4,2 , - 1 , \frac { 1 } { 2 } ,8,−4,2,−1,21​,

Find a General Term A_n for the Geometric Sequence $8 , - 4,2 , - 1 , \frac { 1 } { 2 } ,$