Question

In a certain A.P. the 24^th term is twice the 10^th term. Prove that the 72^nd term is twice the 34^th term.

Answer 1

Given,

24^th term is twice the 10^th term.

We know that, n^th term a_n = a + (n – 1)d

⇒ a₂₄ = 2(a₁₀)

a + (24 – 1)d = 2(a + (10 – 1)d)

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

a + 23d = 2a + 18d

a = 5d …. (1)

Now, the 72^nd term can be expressed as

a₇₂ = a + (72 – 1)d

= a + 71d

= a + 5d + 66d

= a + a + 66d [using (1)]

= 2(a + 33d)

= 2(a + (34 – 1)d)

= 2(a₃₄)

⇒ a₇₂ = 2(a₃₄)

Hence, the 72^nd term is twice the 34^th term of the given A.P.