Which term of the GP 3, 6, 12, 24…. Is 3072?

Solution:

Given GP is 3, 6, 12, 24….

The given GP is of the form, $a, a r, a r^{2}, a r^{3} \ldots .$

Where r is the common ratio.

First term in the given GP, a1 = a = 3

Second term in GP, a2 = 6

Now, the common ratio, $r=\frac{a_{2}}{a_{1}}$

$r=\frac{6}{3}=2$

Let us consider 3072 as the $\mathrm{n}^{\text {th }}$ term of the GP.

Now, $n^{\text {th }}$ term of GP is, $a_{n}=a r^{n-1}$

$3072=3.2^{n-1}$

$\frac{3072 \times 2}{3}=2^{n}$

$2^{n}=2^{11}$

$n=11$

So, 3072 is the $11^{\text {th }}$ term in GP.