Question

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

Answer 1

Given: 5th, 8th and 11th terms of a G.P. are p, q and s, respectively

We know that in G.P an = arn-1

Here, n: number of terms

a: First term

r: common ratio

Here,

a5 = ar5-1 = ar4

⇒ p = ar4 (∵ 5th term of G.P. is given p) –1

Similarly,

a8 = ar8-1 = ar7

⇒ q = ar7 (∵ 7th term of G.P. is given q) –2

a11 = ar11-1 = ar10

⇒ s = ar10 (∵ 11th term of G.P. is given s) –3

We can observe that:

q × q = p × s (that is, ar7 × ar7 = ar4 × ar10)

∴ q2 = ps

Hence proved

JAI SHREE KRISHNA