Question

Find $a_{20}$ of a geometric sequence, if the first few terms of the sequence are given by $-\frac{1}{2},\frac{1}{4},-\frac{1}{8},\frac{1}{16},\cdots$

• A. ${20}^{20}$
• B. $\frac{1}{2^{20}}$
• C. $\frac{1}{20}$
• D. $\frac{1}{2^{19}}$

Answer 1

The correct option is B

$\frac{1}{2^{20}}$

We first find the common ratio $r$ of the GP.
$r=\frac{a_2}{a_1}=\frac{\frac{1}{4}}{-\frac{1}{2}}=-\frac{1}{2}$
Since the $n^{\text{th}}$ term of the GP is given by
$a_n=a_1{r}^{n-1},$ we have
$a_{20}=(-\frac{1}{2})\times {(-\frac{1}{2})}^{20-1}=\frac{1}{2^{20}}.$