Question

Which term of the GP $3,3\sqrt{3},\mathrm{9....}$ is $2187$ ?

• A. 15
• B. 14
• C. 13
• D. 19
• E. 20

Answer 1

Answer: (C)

Let nth term of GP is 2187 $\therefore$
$3{(\sqrt{3})}^{n-1}=2187$
$\Rightarrow$ $3^{(n/2-1/2+1)}=3^7$
$\Rightarrow$ $\frac{n}{2}+\frac{1}{2}=7$
$\Rightarrow$ $n=13$