Question

How do you write the expression for the nth term of the sequence given `3, 7, 11, 15, 19,...`?

Answer 1

`4n -1`

Explanation:

`3 , 7 , 11 , 15 ,19 ...`
is an arithmetic sequence. All arithmetic sequences can be written in the form `a + (n-1)d` where `a` is the first term in the sequence and `d` is the common difference . `n` represents the required term.

From example `a = 3 , d = 4` :

Hence `3 + (n - 1)4`

Expanding `3 + 4n - 4`

Collecting like terms `4n - 1`:

To check: The 4th term is `4` x `4 - 1 = 15`