Question

The 24^th term of an A.P. is twice its 10^th term. Show that its 72^nd term is 4 times its 15^th term.

Answer 1

Given:

a₂₄ = 2a₁₀

a +23d = 2(a +9d)

5d = a (i)

To Prove:

a₇₂ = 4a₁₅

Proof:

L.H.S. = a₇₂

= a +71d

= 5d +71d [from (i)]

= 76d

R.H.S = 4a₁₅

= 4(a +14d)

= 4a +56d

= 4(5d) +56d [from (i)]

= 20d +56d

= 76d

Since, L.H.S = R.H.S.

Hence proved