Question

If 8th term of an A.P. is zero, prove that its 38th term is triple of its 18th term.

Answer 1

T₈ = 0
To prove that T₃₈ = 3 x T₁₈
Let a be the first term and d be the common difference
∴ T₈ = a + 7d = 0
⇒ a = –7d
Now
T₃₈ = a + 37d
= –7d + 37d
= 30d
and
T₁₈ = a + 17d
= –7d + 17d
= 10d
It is clear that T₃₈ is triple of T₁₈.