Question

if the 8th term of an APis 0then prove that it's 38th term is triple of its 18th term

Answer 1

let a is the first term and d is the common difference of AP

now,
8th term =0
a + (8 - 1) d = 0
a + 7d =0
a = -7d

a/c to question ,
prove that
38 th term = 3 x 18th term

LHS = 38th term
=a +(38-1)d = a + 37d

put a = -7d

now ,
LHS = -7 d + 37d = 30 d

RHS =3 {18th term }
=3 { a +(18-1) d }

now put a = -7d
=3 { -7d +17d } = 30d

LHS = RHS
hence proved

Answer 2

a+7d=0
a=-7d

18th term =a+17d
-7d+17d=10d

38th term =a+37d
-7d+37d=30d
30d=3(10d)

38th term= 3*10term