UPSC NDA Math Model Paper 4

Given: The 4th and 9th term of a GP are 54 and 13122 respectively.
As we know that, the general term of a GP is given by: an=arn−1.
Let a be the first term and r be the common ratio.
⇒a4=a.r3=54 .......(1)
⇒a9=a.r8=13122 .........(2)
On dividing (2) by (1) we get,
⇒

a.r8

a.r3

=

13122

54

⇒r5=243=35
⇒r=3
By substituting r = 3 in (1), we get
⇒a.(3)3=54
⇒a=2
As we know that, the general term of a GP is given by: an=arn−1
Hence, the general term of the given GP is: 2.3(n−1)