# Find the nth term of a sequence whose first several terms are given. {eq}1, 5, 9, 13,... {/eq}

## Question:

Find the nth term of a sequence whose first several terms are given.

{eq}1, 5, 9, 13,... {/eq}

## Arithmetic Sequence:

An arithmetic sequence has a constant difference between successive terms.

If {eq}a{/eq} is the initial term and {eq}d{/eq} is the common difference then the nth term will be given by,

{eq}t_n=a+(n-1)d{/eq}

We can determine {eq}a{/eq} and {eq}d{/eq} for the given problem.

Then using the formula above we can find the nth term of given sequence.

Given sequence,

{eq}1, 5, 9, 13, ... {/eq}

First term of the sequence is {eq}a=1{/eq}

The difference between successive terms is constant and given by {eq}d=4{/eq}.

Hence given sequence is an arithmetic sequence with,

a=1, d=4

{eq}\begin{align} \text{nth term }&= a+(n-1)d \\ t_n &=1+(n-1)(4) \\ \color{blue}{t_n} & \color{blue}{=4n-3} \end{align} {/eq}