Question

I am having a hard time understanding explicit formulas with arithmetic sequences. The current sequence I am working with is:2, 8, 14, 20, 26The common difference is 6. I don't know how to come up with the explicit formula when given the sequence.

Answer 1

we are given the sequence

`2,8,14,20,26,..`

The first term = 2

Common difference = 6

The sequence is an arithmetic progression

The nth term is given as

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

Therefore, the answer is

`a_(n)=6n-4`