# The first term of a G.P is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P

**Solution:**

Let a and r be the first term and common ratio of the G.P respectively.

Hence,

a = 1

a_{3} = ar^{2} = r^{2}

a_{5} = ar^{4} = r^{4}

Therefore,

r^{2} + r^{4} = 90

r^{2} + r^{4} - 90 = 0

r2 = (1 ± √1 + 360) / 2

= - 1 ± √361) / 2

= (- 1 ± 19) / 2

= - 10 or 9

r^{2} = 9 [Taking real roots]

r = ± 3

Thus, the common ratio of the G.P is ± 3

NCERT Solutions Class 11 Maths Chapter 9 Exercise ME Question 9

## The first term of a G.P is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P

**Summary:**

It is known that the first term of a G.P is 1 and the sum of the third and fifth term is 90, therefore the common ratio comes out to be r = ± 3

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