Question

If 4th term of an AP is 0. Prove that 25th term is triple the 11th term

Answer 1

a^25 = 3 x a^11 .

Explanation:

Given a^4 = 0

That is (a + 3d) = 0

⇒ a = - 3d ........... (1)

nth term of AP is given by an = a + (n – 1)d

a^11 = a + 10d = – 3d + 10d = 7d [From (1)]

a^25 = a+ 24d = – 3d + 24d = 21d [From (1)]

Hence

The answer is a^25=3 x a^11

Answer 2

The 4th term = a+3d = 0,

or a = -3d.

The 25th term = a+24d = -3d+24d = 21d. ...

the 25th term is 3 times the 11th term. Proved.