# The 5^{th}, 8^{th} and 11^{th} terms of a G.P are p, q and s respectively. Show that q^{2} = ps

**Solution:**

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

According to the question,

a_{5} = ar^{5 }^{- }^{1} = ar ^{4} = p ....(1)

a_{8} = ar^{8 }^{- }^{1} = ar^{7} = q ....(2)

a_{11} = ar^{11 }^{- 1} = ar^{10} ....(3)

Dividing (2) by (1) , we obtain

ar^{7}/ar^{4} = q/p

r^{3} = q/p ....(4)

Dividing (3) by (2) , we obtain

ar^{10}/ar^{7} = s/q

r^{3} = s/q ....(5)

Equating the values of r^{3} obtained in (4) and (5), we obtain

⇒ q/p = s/q

⇒ q^{2} = ps

Hence proved

NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.3 Question 3

## The 5^{th}, 8^{th} and 11^{th} terms of a G.P are p, q and s respectively. Show that q^{2} = ps

**Summary:**

It is given that the 5^{th}, 8^{th} and 11^{th} terms of a G.P are p, q and s respectively and we showed that q^{2} = ps