Question

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

Answer 1

a +7d= 0
a= -7d
as its the 38th term 
a₃₈ = a +37d
= -7d + 37d 
= 30d
for the 18th term
a₁₈= a +17d
= -7d + 17d
= 10d
so a₃₈ = 3a₁₈

Answer 2

"a(8) = a+7d, where a is the first term and d is the common difference.

a+7d=0

a=-7d

A +7d= 0

a= -7d

As is the 38th term

a₃₈ = a +37d

= -7d + 37d

= 30d

a(38) = a+37d = -7d+37d = 30d

a(18)=a+17d = -7d+17d = 10d

30 d = 3 times 10 d

38th term is triple its 18th term

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