Question

The $4th$ terms of an A.P. is zero. Prove that the its $25th$ term is triple its $11th$ term.

Answer 1

Let first term of an A.P=$a$

common difference of A.P=$d$

According to question,

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

25th term =$a+24d$

from (1)...$a=-3d$

=> $-3d+24d$

=> $21d$.....(2)

11th term=$a+10d$

=$-3d+10d$

=$7d$.....(3)

By (3) and(2) 25th term=$3\times$ 11th term

Hence proved