Question

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

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

Answer 1

Correct Answer - Option 3 : 24

Concept :

Let us consider sequence a₁, a₂, a₃ …. a_n 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  a_n = ar^n-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 5^th term of G.P is 96 

i.e  a₅ = ar^5-1 

⇒ a₅ = ar⁴ 

⇒ 96 = ar⁴        ----( i ) 

Given: 8th term is 768

⇒ a8 = ar7 

768 = ar⁷       ----(ii) 

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

8 = r³ 

⇒ r = 2 .

Putting this in eqn. (i) , we get 

a = 6 .

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

So, a₃ = 6× 2^3-1 

⇒ a₃ = 24 . 

The correct option is 3.