Question

In a certain A.P. the 24^th term is twice the 10^th term. Prove that the 72^nd term is twice the 34^th term.

Answer 1

Given:

a₂₄ = 2a₁₀

To Prove:

a₇₂ = 2a₃₄

Proof:

a₂₄ = 2a₁₀

a + (24 –1)d = 2a + 2(10 –1)d

23d – 18d = a

a = 5d

LHS= a₇₂ = a + 71d = 5d +71d = 76d

RHS = a₃₄ = 2a + 2(33)d = 10d + 66d = 76d

Since, LHS = RHS

Hence, proved