Question

Find the common difference and write the next four terms of each of the following arithmetic progressions:

`-1, 1/4, 3/2 .....`

Answer 1

`-1, 1/4, 3/2 .....`

Here, first term (a₁) =−1

Common difference (d)  = `a_2 - a_1`

`= 1/4 - (-1)`

`=- (1 + 4)/4`

= 5/4

Now, we need to find the next four terms of the given A.P

That is we need to find  `a_4, a_5, a_6, a_7`

So using the formula `a_n = a + (n -1)d`

Substituting  n = 4, 5, 6, 7 in the above formula

Substituting n = 4, we get

`a_4 = -1 + (4 -1)(5/4)`

`a_4 = -1 + 15/4`

`a_4 = (-4 + 15)/4`

`a_4 = 11/4`

Substituting n = 5, we get

`a_5 = -1 + (5 - 1)(5/4)`

a_5 = - 1 + 5`

`a_5 = 4`

Substituting n = 6, we get

`a_6 = -1 + (6 - 1)(5/4)`

`a_6 = -1 + 25/4`

`a_6 = (-4 + 25)/4`

`a_6 = 21/4`

Substituting n = 7, we get

`a_7 = -1 + (7 -1) (5/4)`

`a_7 = -1 + 30/4`

`a_7 = (-4 + 30)/4`

`a_7 = 26/4`

Therefore, the common difference is `d = 5/4` and the next four term are `11/4 , 4. 21/4 , 26/4`