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

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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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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.