Question

For the sequence of numbers

Work out the position to term rule

22, 23, 24, 25, .......

Answer 1

The term rule will be:

`a_n=n+21`

Explanation:

Given the sequence

`22, 23, 24, 25, ...`

Computing the common difference of all the adjacent terms

`22,\:23,\:24,\:25`

`23-22=1,\:\quad \:24-23=1,\:\quad \:25-24=1`

As the difference between all the adjacent terms is the same and equal to

`d=1`

The first element of the sequence

`a_1=22`

We know that An Arithmetic sequence has a constant difference 'd' and is defined by

`a_n=a_1+\left(n-1\right)d`

substituting
`a_1=22`, and
`d=1` in the nth term to get the term rule

`a_n=a_1+\left(n-1\right)d`

`a_n=\left(n-1\right)+22`

`a_n=n+21`

Therefore, the term rule will be:

`a_n=n+21`