The 5^th, 8^th and 11^th terms of a G.P are p, q and s respectively. Show that q² = ps

Solution:

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

According to the question,

a₅ = ar^{5 - 1} = ar ⁴ = p ....(1)

a₈ = ar^{8 - 1} = ar⁷ = q ....(2)

a₁₁ = ar^{11 - 1} = ar¹⁰ ....(3)

Dividing (2) by (1) , we obtain

ar⁷/ar⁴ = q/p

r³ = q/p ....(4)

Dividing (3) by (2) , we obtain

ar¹⁰/ar⁷ = s/q

r³ = s/q ....(5)

Equating the values of r³ obtained in (4) and (5), we obtain

⇒ q/p = s/q

⇒ q² = ps

Hence proved

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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 q² = 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 q² = ps