Question

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

0, –3, –6, –9,...

Answer 1

In the given problem, we need to find the common difference and the next four terms of the given A.P.

0, −3, −6, −9,...

Here, first term (a₁) = 0

Common difference (d) = `a_2 - a_1`

= -3 - 0

= -3

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

That is we need to find  `a_5,a_6,a_7,a_8`

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

Substituting  n = 5, 6, 7, 8 in the above formula

Substituting n = 5, we get

`a_5 = 0 + (5 - 1)(-3)`

`a-5 = 0 - 12`

`a_5 =-12`

Substituting n = 6, we get

`a_6 = 0 + (6 - 1)(-3)`

`a_6 = 0 - 15`

`a_6 = -15`

Substituting n = 7, we get

`a_7 = 0 + (8 - 1)(-3)`

`a_8 = 0 - 21`

`a_8 = -21`

Therefore, the common difference is d = -3 and the next four terms are -12, -15, -18, -21