Question

The first term of a geometric series is 1. The sum of its third and fifth terms is 90. Find the ratio of the geometric series​

Answer 1

Step-by-step explanation:

Let r be the common ratio of the G.P. It is given that the first term a=1.

Now, a

3

+a

5

=90

⇒ar

2

+ar

4

=90

⇒r

2

+r

4

=90

⇒r

4

+r

2

−90=0

⇒r

4

+10r

2

−9r

2

−90=0

⇒(r

2

+10)(r

2

−9)=0

⇒r

2

−9=0

⇒r=±3

Hence, the common ratio of the given G.P. is 3 or −3.