Question

What is the common difference of an A.P. in which a₂₁ – a₇ = 84?

Answer 1

Let a be the first term and d be the common difference of AP.

We know that

an = a +(n − 1)d

∴ a₂₁ = a +(21 − 1)d = a + 20d

and a₇=a + (7 − 1)d = a + 6d

Given:

a₂₁ − a₇ = 84

∴ (a + 20d) − (a + 6d) = 84

⇒ a + 20d − a − 6d = 84

⇒14d = 84

⇒ d = 6

Thus, the common difference of the AP is 6