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In a G.P , the 5th term is 96 and 8th term is 768, then the 3rd term of G.P is  ?


1. 16
2. 48
3. 24
4. 36

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Best answer
Correct Answer - Option 3 : 24

Concept :

Let us consider sequence a1, a2, a3 …. an is a G.P.

  • Common ratio , r = \(\rm \frac{a_{2}}{a_{1}} = \frac{a_{3}}{a_{2}}= ... = \frac{a_{n}}{a_{n-1}}\) 
  • \(\rm n^{th}\) term of G.P  is  an = arn-1 
  • Sum of n terms = s = ; where r >1
  • Sum of n terms = s = ; where r <1 
  • Sum of infinite GP = \(\rm s_{\infty }= \frac{a}{1-r}\) ; |r| < 1


Calculation :  

Here 5th term of G.P is 96 

i.e  a5 = ar5-1 

⇒ a5 = ar4 

⇒ 96 = ar4        ----( i ) 

Given: 8th term is 768

⇒ a8 = ar7 

768 = ar7       ----(ii) 

Divide eqn. (ii) by eqn. (i) , we get 

8 = r

r = 2 .

Putting this in eqn. (i) , we get 

a = 6 .

We know that , \(\rm n^{th}\) term of G.P , an = arn-1 

So, a3 = 6× 23-1 

a3 = 24 . 

The correct option is 3. 

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