Question

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

Answer 1

Proof :

Let, the first term of the AP is a and the common difference is d.

Then, n-th term = a + (n - 1)d

  • 24th term = a + (24 - 1)d = a + 23d

  • 10th term = a + (10 - 1)d = a + 9d

  • 72nd term = a + (72 - 1)d = a + 71d

  • 34th term = a + (34 - 1)d = a + 33d

By the given condition,

   24th term = 2 × 10th term

⇒ a + 23d = 2 (a + 9d)

⇒ a + 23d = 2a + 18d

⇒ 2a - a = 23d - 18d

⇒ a = 5d

  • 72nd term = a + 71d = 5d + 71d = 76d

  • 34th term = a + 31d = 5d + 33d = 38d

∴ 72nd term = 2 × 34th term

Hence, proved.

Answer 2

the solution is in below pic