Correct Answer - Option 2 : 3072
Concept:
Let us consider sequence a1, a2, a3 …. an is a G.P.
- Common ratio = r = \(\frac{{{{\rm{a}}_2}}}{{{{\rm{a}}_1}}} = \frac{{{{\rm{a}}_3}}}{{{{\rm{a}}_2}}} = \ldots = \frac{{{{\rm{a}}_{\rm{n}}}}}{{{{\rm{a}}_{{\rm{n}} - 1}}}}\)
- nth term of the G.P. is an = arn−1
Calculation:
Here 6th term = a6 = 48
⇒ ar5 = 48 ....(1)
And 12th term = a12 = 384
⇒ ar11 = 384 ....(2)
Dividing eq. (2) by eq.(1) , we get
r6 = 8
Now 18th term of GP = a18 = ar18 - 1 = ar17 = ar11 × r6
= 384 × 8 = 3072