Question

For the sequence of numbers

Answer 1

Answer:

The term rule will be:

$a_n=n+21$

Step-by-step 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:

$a_n=n+21$