Question

If 4th term and 6th term of a G.P. are 64 and 256 respectively,. find the G.P.​

Answer 1

Given: a  

4

​

=54,a  

9

​

=13122 of a G.P.

⇒ar  

3

=54[∵a  

n

​

=ar  

n−1

]...(1)

and a  

9

​

=13122

⇒ar  

8

=13122...(2)

Divide (2) by (1), we get

ar  

3

 

ar  

8

 

​

=  

54

13122

​

 

⇒r  

5

=243

⇒r=3

Now, put the value of r=3 in (1), we get

a×3  

3

=54

⇒a=2

So, a  

6

​

=ar  

5

=2×3  

5

=2×243=486

Answer 2

4th term and 6th term = 192