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.

Question

Philoid · Accepted Answer

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

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