Question

Work out an expression for the nth term for this sequence:

23,35,47,49

Answer 1

`a_n = 23 +12(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
`23` so
`a_1 = 23`.

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 = 35 -23 \\ d = 12`.

Now let's plug everything we know.

`a_1 = 23`

`d = 12`

`a_n = 23 + 12(n -1)`