formula of a sequence when numbers are consistently different

Use the following mnemonic:

or in more detail

1. Find the consistent difference and multiply by `n` (`n` = term position)
2. Find the value before the first term (what would the value be if it were there)
3. Add the two together

Summary

Full value of the `n`^th`` = common different x `n` + term before first term.

Or

Formula for `n`^th term = difference x `n` + (first term — difference).

For further detail go here.

Note:

1. This makes it easy to remember that an even number sequence is:

`2n`

i.e. `2  4  6  8`

Common difference x `n` + term before first term

`2` x `n + 0 = 2n`

2. This makes it easy to remember that an even number sequence is 

`2n - 1`

i.e. `1  3  5  7`

Common difference x `n` + term before first term

`2`  x  `n  (-1) = 2n - 1`

3. Note that for ease of calculation in an exam odd number sequence (so not dealing with negatives) is 

`2n + 1`

i.e. `3  5  7  9` (i.e. miss out `1`)

Common difference x `n` + term before first term

`2`  x  `n + 1 = 2n + 1`