Question

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

`-1, (-5)/6, (-2)/3`

Answer 1

`-1, (-5)/6, (-2)/3`

Here, first term (a₁) =−1

Common difference (d)  = `a_2 - a_1`

`= -5/6 - (-1)`

`= (-5 + 6)/6`

`= 1/6`

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) (1/6)`

`a_4 = -1 + (1/2)`

`a_4 = (-2 + 1)/2 = (-1)/2`

Substituting n = 5, we get

`a_5 = -1 + (5 -1)(1/6)`

`a_5 = - 1 + 2/3`

`a_5 = (-3 + 2)/3`

`a_5 = - 1/3`

Substituting n = 6, we get

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

`a_6 = -1 + 5/6``

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

`a_6 = - 1/6`

Substituting n = 7, we get

`a_7 = -1 + (7 -1) (1/6)`

`a_7 = -1 + 1`

`a_7 = 0`

Therefore, the common difference is `d = 1/6` and the next four terms are `-1/2, -1/3, -1/6,0`