Question

If $4^{th}$ term of a GP is $32$ whose common ratio is half of the first term, then the ${15}^{th}$ term is

• A. $2^{12}$
• B. $2^{18}$
• C. $2^{14}$
• D. $2^{16}$
• E. $2^{10}$

Answer 1

Answer: (D)

$2^{16}$

Let first term and common ratio of GP be $a$ and $r$, respectively.
Then, $r=\frac{1}{2}a$
Now, $a_4=32$
$\Rightarrow a{r}^3=32$
$\Rightarrow a{\left(\frac{1}{2}a\right)}^3=32$
$\Rightarrow a^4=256$
$\Rightarrow a=4$
$\Rightarrow r=\frac{1}{2}a=\frac{1}{2}\times 4=2$
Hence, $a_{15}=a{r}^{14}=4{\left(2\right)}^{14}=2^{16}$