Question

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

Answer 1

In the given AP, let the first be a and the common difference be d.
Then,  t_n = a + (n-1)d

Now , T₄  = a + (4-1) d

⇒  a +3d = 0          ....................(1)

⇒ a = -3d 

Again  T₁₁ = a + (11-1) d = a + 10 d

= -3d + 10d =  7d                [ Using (1)]

Also , T₂₅  = a + ( 25-1) d = a + 24d = - 3d + 24 d = 21d       [Using (1)] 

 i.e . , T₂₅ = 3 × 7d = ( 3 × T ₁₁)

Hence, 25^th term is triple its 11^th term.