Question

2,-2,-6,-10,-14, ...how do I go about finding the explicit formula?

Answer 1

According to the given sequence, the difference is -4, because it's decreasing with that difference: 2-2 = -2; -2-4 = -6; and so on.

To find the explicit formula, we use the arithmetic sequence formula.

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

Replacing all the given information, we have.

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

This explicit formula we can also express as

`f(n)=6-4n`