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

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

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