Write the expression for the general (or nth)termrm, $\mathbf { a } _ { \mathbf { n } } ,$ , of the geometric sequence.
-$2,1 , \frac { 1 } { 2 } , \frac { 1 } { 4 } , \ldots$
A) $a _ { n } = \frac { 1 } { 2 } ( 2 ) ^ { n - 1 }$
B) $a _ { n } = 2 \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$
C) $a _ { n } = 2 ( 2 ) ^ { n - 1 }$
D) $a _ { n } = 2 \left( \frac { 1 } { 4 } \right) ^ { n - 1 }$

Question

Quizplus · Accepted Answer

The sequence is a geometric sequence with the first term $a_1 = 2$ and common ratio $r = \frac{1}{2}$. The formula for the nth term of a geometric sequence is $a_n = a_1 \cdot r^{n-1}$, which matches choice B when $a_1 = 2$ and $r = \frac{1}{2}$.

Write the Expression for the General (Or Nth)termrm an,\mathbf { a } _ { \mathbf { n } } ,an​,

Write the Expression for the General (Or Nth)termrm $\mathbf { a } _ { \mathbf { n } } ,$