Question

The 4th term of an ap is zero prove that 25th term of an ap is 3 times its 11th term

Answer 1

aₓ=a₁+(x-1)d
a₄=a₁+3d=0
a₂₅=a₁+24d=21d
a₁₁=a₁+10d=7d
a₂₅=3.a₁₁

Answer 2

Given a4= 0


i.e. (a + 3d) = 0

⇒ a = - 3d (1)

nth term of AP = a + (n – 1)d

a11= a + 10d = – 3d + 10d =7d [From (1)]

a25= a+ 24d

= – 3d + 24d

= 21d [From (1)]

= 3 x 7d


Hence a25= 3 x a11


Hope it will help