Question

If 10 times the 10th term of an A.P. is equal to 15 times the 15th term, show that 25th term of the A.P. is zero.

Answer 1

According to question ,
10 x 10th term =15 x 15th term
Let $a$ is the first term and $d$ is the common difference.

$10[a+(n-1\left)\right]d=15[a+(n-1\left)\right]d$

$\Rightarrow 10(a+9d)=15(a+14d)$
$\Rightarrow 5a+120d=0$
$\Rightarrow a+24d=\mathrm{0...}\left(i\right)$
Now,
25th term

$=a+(25-1)d=a+24d=0$
Hence, 25th term=0 [From (i)]