Question

Two A.P.s have the same common difference. If the difference between their 25th terms is 8, the difference between their 50th terms is ______.

Options

• 16

• 5

• 8

• 25

Answer 1

Two A.P.s have the same common difference. If the difference between their 25th terms is 8, the difference between their 50th terms is 8.

Explanation:

Let A and a are the first terms of two given A.P's with common difference d.

T₂₅ – T₂₅ = 8

`\implies` (a₁ + 24d) – (a₂ + 24d) = 8   ...[∵ T_n = a + (n – 1)d]

`\implies` a₁ – a₂ = 8  ...(1)

∴ T₅₀ – T₅₀ = (a₁ + 49d) – (a₂ + 49d)

= a₁ – a₂

= 8