Question

A. The first 5 terms of a sequence are given. Use these terms to answer the following questions. 2, 8, 14, 20, 26Write an explicit rule to represent the arithmetic sequence. Be sure to define your variables and explain how you got your answer.

Answer 1

Notice that the sequence has a common difference of 6 units, then, using the following formula:

`a_n=a_1+(n-1)d`

where a1 is the first term and d is the common difference. Then, in this case we have the following:

`\begin{gathered} d=6 \\ a_1=2 \\ \Rightarrow a_n=2+(n-1)\cdot6=2+6n-6 \\ =6n-4 \\ a_n=6n-4 \end{gathered}`

therefore, the explicit rule is an=6n-4