Question

the 8th term of AP is zero then prove that its 38 term is triple its 18 term

Answer 1

a8 = 0.
a + 7d = 0 ......................1st equation
to prove :-
a 38 = 3 * a18
LHS = a 38
= a + 37d
= a + 7d + 30d 
= 30d            .........since a + 7d = 0.

Now,
RHS = 3 a18
= 3 * ( a + 17d)
= 3a + 51d
= 3a+ 21d + 30d
= 3 (a+7d) + 30d
= 3 * 0 + 30d
=30d

therfore,
LHS = RHS.
hence proved that a38 = 3 * a18 in the ap where a8 = 0.

hope this helps...........