Q17 of 176 Page 21

If the p^th and q^th terms of a G.P. are q and p respectively, show that (p + q)^th term is

Given: p^th and q^th terms of a G.P. are q and p

Formula Used: T_n = arⁿ^-1

So, we get,

q = ar^p-1 …(1)

p = ar^q-1…(2)

To Prove:

Proof:

Divide (1) by (2), we get

⇒

Substituting we get,

⇒

L.H.S = ar^p+q-1

L.H.S = R.H.S

Hence, Proved.

If a, b, c, d and p are different real numbers such that :

(a² + b² + c²)p² – 2(ab + bc + cd) p + (b² + c² + d²) ≤ 0, then show that a, b, c and d are in G.P.

If then show that a, b, c, and d are in G.P.

Find three numbers in G.P. whose sum is 65 and whose product is 3375.

Find three number in G.P. whose sum is 38 and their product is 1728.

If the pth and qth terms of a G.P. are q and p respectively, show that (p + q)th term is