Question

Work out the nth of this sequence:

Answer 1

`a_n = -11 +3(n -1)`

Step-by-step explanation:

The
`n`th term of an arithmetic sequence is explicitly defined as
`a_n = a_1 +d(n -1)` where
`a_1` is the first term of the sequence and
`d` is the the common difference.

From the given first five terms of the sequence we can see that the first term is
`11` so
`a_1 = 11`.

The common difference,
`d`, can be calculated by
`a_n - a_(n -1)` so we'll find the common difference of the given sequence by letting
`n = 2`

`d = a_2 - a_(2 -1) \\d = a_2 -a_(1) \\d = -8 -(-11) \\ d = -8 +11 \\ d = 3`.

Now let's plug everything we know.

`a_1 = -11`

`d = 3`

`a_n = -11 +3(n -1)`