Question

The 4th term of an AP is zero. Prove that its 25th term is triple its 11th term.

Answer 1

We know that nth term of an AP an = a + (n - 1) * d.

Now,

(i)

Given 4th term of an AP is 0.

⇒ a4 = a + (4 - 1) * d

⇒ 0 = a + 3d

⇒ a = -3d.

(ii)

⇒ 11th term = a + (11 - 1) * d

                   = a + 10d

                   = -3d + 10d

                   = 7d

(iii)

⇒ 25th term = a + (25 - 1) * d

                     = a + 24d

                     = -3d + 24d

                     = 21d

                     = 3 * a11.

Therefore, 25th term of an AP is triple its 11th term.

Hope this helps!