Question

Which term of the $GP3,3\sqrt{3},\mathrm{9..}$ is $2187$?

• A. $15$
• B. $14$
• C. $13$
• D. $19$

Answer 1

The correct option is C $13$

Given G.P series: $3,3\sqrt{3},\mathrm{9...}$

Common ratio (r) of the above given series:

$r=\frac{3\sqrt{3}}{3}$

$r=\sqrt{3}$

Let the rth term of the given G.P series is $2187$.

Apply the formula: $T_{r}=a(r)^{n-1}$

$2187=3(\sqrt{3}{)}^{n-1}$

$\frac{2187}{3}=(\sqrt{3}{)}^{n-1}$

$729=(\sqrt{3}{)}^{n-1}$

($3{)}^6=(\sqrt{3}{)}^{n-1}$

$(\sqrt{3}{)}^{12}=(\sqrt{3}{)}^{n-1}$

$12=n-1$

$n=13$

The 13th term of the given G.P will be $2187$.

Option (C) is correct.