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In a GP  the 6th term is 48 and 12th term is 384 , then find its 18th term ?
1. 2072
2. 3072
3. 3426
4. 3428

1 Answer

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Best answer
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

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