Question

In an A.P., a_n – a_{n – 4} = 32. Its common difference is ______.

Options

• –8

• 8

• 4n

• 4

Answer 1

In an A.P., a_n – a_{n – 4} = 32. Its common difference is 8.

Explanation:

Given, a_n – a_{n – 4} = 32

We know that, n term of an A.P.:

a_n = a + (n – 1) × d   ...(1)

And (n – 4) term of an A.P.

a_{n – 4} = a + (n – 4 – 1) × d

= a + (n – 5) × d   ...(2)

Now, putting the value from equation (1) and equation (2),

a_n – a_{n – 4} = 32

⇒ a + (n – 1) × d – [a + (n – 5) × d] = 32

⇒ a + nd – d – a – nd + 5d = 32

⇒ 4d = 32

⇒ d = `32/4`

⇒ d = 8

Therefore, the common difference of A.P. is 8.