Find a general term an for the geometric sequence.
-$$\mathrm { a } _ { 1 } = \frac { 1 } { 2 } , \mathrm { r } = 2$$
A) $a _ { n } = \frac { 1 } { 2 } \cdot 2 ^ { n - 1 }$
B) $a _ { n } = \left( \frac { 1 } { 2 } \right) n - 1 + \frac { 1 } { 2 }$
C) $\mathrm { a } _ { \mathrm { n } } = \frac { 1 } { 2 } + \frac { 1 } { 2 } ( \mathrm { n } - 1 )$
D) $a _ { n } = \frac { 1 } { 2 } + 2 ( n - 1 )$

Question

Quizplus · Accepted Answer

The general term of a geometric sequence is given by $a_n = a_1 \cdot r^{n-1}$, where $a_1$ is the first term and $r$ is the common ratio. Here, $a_1 = \frac{1}{2}$ and $r = 2$, so $a_n = \frac{1}{2} \cdot 2^{n-1}$.

Find a General Term an for the Geometric Sequence a1=12,r=2\mathrm { a } _ { 1 } = \frac { 1 } { 2 } , \mathrm { r } = 2a1​=21​,r=2

Find a General Term an for the Geometric Sequence $\mathrm { a } _ { 1 } = \frac { 1 } { 2 } , \mathrm { r } = 2$