#### Question

What is the common difference of an A.P. in which a_{21} – a_{7} = 84?

#### Solution

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

We know that

an = a +(n − 1)d

∴ a_{21} = a +(21 − 1)d = a + 20d

and a_{7}=a + (7 − 1)d = a + 6d

Given:

a_{21} − a_{7} = 84

∴ (a + 20d) − (a + 6d) = 84

⇒ a + 20d − a − 6d = 84

⇒14d = 84

⇒ d = 6

Thus, the common difference of the AP is 6

Is there an error in this question or solution?

Solution What is the Common Difference of an A.P. in Which A21 – A7 = 84? Concept: Arithmetic Progression.