Two APs have the same common difference. The first term of one of these is - 1 and that of the other is - 8. The difference between their 4th terms is?

Given: a = - 1

A = - 8

To find: a₄ -A₄

Formula Used: nth term of an AP is:

a_{n =} a + (n - 1) d

Explanation:

Let a and A be the first terms of Two AP’s.

a = - 1

A = - 8

Let d and D be the common differences of two AP’s.

D = d ……. (i)

Let a₄ and A₄ be the 4^th terms of two AP’s.

As we know, nth term of an AP is

a_{n =} a + (n - 1) d

where a = first term

a_n is nth term

d is the common difference

a₄ -A_{4 =} a + 3d – (A + 3D)

= a + 3d - A - 3d (using ( i ) )

= a - A

= - 1 - (- 8)

= -1 + 8

= 7