Answer:

Given,

24^th term is twice the 10^th term

a₂₄ = 2a₁₀

a_n = a + (n – 1) d

When n = 10,

a₁₀ = a + (10 – 1)d

= a + 9d

When n = 24,

a₂₄ = a + (24 – 1)d

= a + 23d

When n = 34,

a₃₄ = a + (34 – 1)d

= a + 33d ………(i)

When n = 72,

a₇₂ = a + (72 – 1)d

= a + 71d

a₂₄ = 2a₁₀

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

a + 23d = 2a + 18d

a – 2a + 23d – 18d = 0

-a + 5d = 0

a = 5d

a₇₂ = a + 71d

a₇₂ = 5d + 71d

= 76d

= 10d + 66d

= 2(5d + 33d)

= 2(a + 33d) [since, a = 5d]

a₇₂ = 2a₃₄ (From (i))

Thus, Proved.