Question

Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.

0, −4, −8, −12, ...

Answer 1

In the given problem, we are given various sequences.

We need to find out that the given sequences are an A.P or not and then find its common difference (d)

0, −4, −8, −12, ...

Here

First term (a) = 0

`a_1 = -4`

`a_2 = -8`

Now, for the given sequence to be an A.P,

Common difference (d) = `a_1 - a = a_2 - a_1`

Here

`a_1 -  a = -4  - 0`

= -4

Also

`a_2 - a_1 = -8 - (-4)`

= -4

Since `a_1 - a = a_2 - a_1`

Hence, the given sequence is an A.P and its common difference is d = -4