Question

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

1, −2, −5, −8, ...

Answer 1

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

1, −2, −5, −8, ...

Here, first term (a₁) =1

Common difference (d) = `a_2 - a_1`

= -2 -1

= -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 we get

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

`a_5 = 1 - 12`

`a_5 = -11`

Substituting n = 6, we get

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

`a_6 = 1 - 15`

`a_6 = -14`

Substituting n = 7, we get

`a_7 = 1 + (7 - 1)(-3)`

`a_7 = 1 - 18`

`a_7 = -17`

Substituting n = 8, we get

`a_8 = 1 + (8 - 1)(-3)`

`a_8 = 1 - 21`

`a_8 = -20`

Therefore, the common difference is d = -3 and the next four terms are -11, -14, -17, -20