Question

The 4 term of an AP is zero, then prove that 25 term of the AP is three times it's 11 term

Answer 1

Given a4 = 0
That is (a + 3d) = 0
⇒ a = - 3d → (1)
nth term of AP is given by an = a + (n – 1)d

a11 = a + 10d = – 3d + 10d = 7d [From (1)](2)
a25 = a+ 24d = – 3d + 24d = 21d [From (1)]
= 3 x 7d
Hence a25 = 3 x a11 {from 2}