Two A.P.s have the same common difference. The first term of one of these is

− 1 and that of the other is − 8. Then the difference between their 4^th  term is:

We are given two A.P.s which have the same common difference. The first term of the first A.P. is 𝑎 =− 1

The first term of the second A.P. is 𝑎' =− 8

Both of them have the same common difference, i.e., 𝑑 = 𝑑'

We have to find the difference between their 4𝑡ℎ terms, i.e., 𝑛 = 4. The formula for 𝑛𝑡ℎ term is, 𝑎 = 𝑎 + (𝑛 − 1)𝑑

So, 𝑎₄ − 𝑎₄ ' = 𝑎 + (𝑛 − 1)𝑑 − [𝑎' + (𝑛 − 1)𝑑']

⇒ 𝑎₄ − 𝑎₄ ' = 𝑎 + (𝑛 − 1)𝑑 − 𝑎' − (𝑛 − 1)𝑑'

⇒ 𝑎₄ − 𝑎₄ ' = 𝑎 − 𝑎' (as 𝑑' = 𝑑)

⇒ 𝑎₄   − 𝑎₄ ' =   − 1 − (− 8)

⇒ 𝑎₄   − 𝑎₄ ' =   − 1 + 8

⇒ 𝑎₄ − 𝑎₄ ' = 7

Hence, the correct option is (c) 7.