Question

Position to term rule of 2, 6, 10, 14, 18

multiply by _____ and subtract by _____

Answer 1

Please check the explanation.

Explanation:

Given the sequence

2, 6, 10, 14, 18

An arithmetic sequence has a constant difference and is defined as

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

compute the differences of all the adjacent terms

`6-2=4,\:\quad \:10-6=4,\:\quad \:14-10=4,\:\quad \:18-14=4`

The difference between all the adjacent terms is the same.

Thus,

`d=4`

and

`a_1=2`

Therefore, the nth term is computed by:

`a_n=4\left(n-1\right)+2`

`a_n=4n-2`

Thus, position to term rule of 2, 6, 10, 14, 18 multiply by __4___ and subtract by __2__.