# Write an expression for the nth term of the sequence. (There is more than one correct answer.) 1,...

## Question:

Write an expression for the {eq}n {/eq}th term of the sequence. (There is more than one correct answer.)

{eq}\displaystyle 1,\ 7,\ 13,\ 19,\ .\ .\ . {/eq}

## Arithmetic sequence:

A sequence of form {eq}a, \ a+d, \ a+2d,... {/eq} is called the arithmetic sequence where {eq}a {/eq} is the first term, {eq}d {/eq} is a common difference. The {eq}n {/eq}th term of the sequence is given by the formula {eq}a_n=a+(n-1)d {/eq} where {eq}a {/eq} is the first term, {eq}d {/eq} is a common difference.

We have the sequence {eq}\displaystyle 1,\ 7,\ 13,\ 19,\ .\ .\ . {/eq}

Here,

First term=1

Second term=7

Third term=13

Consider the difference,

Second term -First term=7-1=6

and Third term -Second term=13-7=6

Thus the given sequence is an arithmetic sequence.

The {eq}n {/eq}th term of the sequence is given by the formula {eq}a_n=a+(n-1)d {/eq} where {eq}a {/eq} is the first term, {eq}d {/eq} is a common difference.

We have {eq}a=1, \ d=6 {/eq}

Therefore the {eq}n {/eq}th term of the given sequence is {eq}1+(n-1)6 \\ =1+6n-6 \\ =6n-5 {/eq}

This is the required {eq}n {/eq}th term.