Question

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

Answer 1

Given, $a_4=0\Rightarrow a+3d=0\Rightarrow a=-3d$

Now, $a_{11}=a+10d=-3d+10d=7d$

and $a_{25}=a+24d=-3d+24d=21d=3\times 7d=3a_{11}$

Hence, proved.