Question

if 8th term is ap is zero proot that its 38 term is triple of its 18 terms

Answer 1

t₈ = 0
a+7d = 0
a = -7d (i)

t₁₈ = a+17d
t₁₈ = -7d+17d
t₁₈ = 10d

t₃₈ = a+37d
t₃₈ = -7d+37d
t₃₈ = 30d
t₃₈ = 3(10d)
t₃₈ = 3(t₁₈)

Hence, proved.

Answer 2

Given, 8th term of an A.P = 0

Formula:

An or Xn = A + (n-1)*d   [An or Xn = last term or Nth term; A - first term,                                

                                        d- common difference, n-number of terms]

8th term = 0

0 = A + (8-1)*d

0 = A + 7*d

A = -7*d .......(i)

Now: 38th term

A38 = A + (38-1)*d

A38 = -7*d + 37*d    [sub value of A from (i)]

A38 = 30*d ......(ii)

18th term:

A18 = A + (18-1)*d

A18 = -7*d + 17*d    [sub value of A from (i)]

A18 = 10*d ......(iii)

Compare (ii) && (iii)

A38 = 30*d && A18 = 10*d

Hence, A38 = 3*10*d = 3*A18

This shows that the 38th term is triple of 18th term. Hence Proved