Question

in an AP ten times the 10th term equals fifteen times the 15th term. prove that the 25th term of the AP is 0

Answer 1

hope it will help you.

Answer 2

Let the first term be a.

Let the second term be d.

We know n th term is a+(n-1)d

So:

10th term=15th term

10[a+(10-1)d]=15[a+(15-1)d]

=10[a+9d]=15[a+14d]

=10a+90d=15a+210d

=10a-15a=210d-90d

=-5a=120d

=a=120/-5*d

=a=-24d

=a+24d=0

=a+(25-1)d=0

So 25 th term is zero since it is a+(25-1)d

Hope it helps you.