Question

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

Answer 1

Let the first term and the common difference be "a" and "d"

Given. T₂₄ = 2 T₁₀

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

= 2a + 18d

or, a = 5d ……………… (i)

Now, T₃₄ = a + 33d

= 5d + 33d Using (i)

= 38d ............. (ii)

T₇₂ = a + 71d

= 5d + 71d Using (i)

= 76d

= 2 x 38d

= 2 x T₃₄ Using (ii)