Question

In any G.P. the first term is $2$ and last term is $512$ and common ratio is $2$, then $5^{th}$ term from end is -

• A. $16$
• B. $32$
• C. $64$
• D. None of these

Answer 1

Answer: (B)

$32$

Since, $a=2,a_n=512,r=2$

$=>a{r}^{n-1}=512\left(2\right)2^{n-1}=5122^{n-1}=256=2^{8}n-1=8\Rightarrow n=9$

Now, $r^{th}$ term from last $=(n-r+1{)}^{th}$ term from starting

$=>5^{th}$ term from last $=(9-5+1{)}^{th}=5^{th}$ term from starting

$=>a_n=a{r}^{n-1}=>a_5=\left(2\right)(2{)}^{5-1}=2^5=32$