Given GP is 3, 6, 12, 24….
The given GP is of the form, a, ar, ar2 , ar3….
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 nth term of the GP.
Now, nth term of GP is, an = arn – 1
3072 = 3.2n-1
\(\frac{3072 \times 2}{3} = 2^n\)
2n = 211n = 11
So, 3072 is the 11th term in GP.