Question

Write a recursive rule for the explicit rule.
an = -4n+ 2​

Answer 1

Check the first few terms:

`a_1 = -4 + 2 = -2`

`a_2 = -8 + 2 = -6`

`a_3 = -12 + 2 = -10`

`a_4 = -16 + 2 = -14`

Note that without fail, there's common difference between consecutive terms of -4. That is,

`a_2 - a_1 = -6 - (-2) = -4`

`a_3 - a_2 = -10 - (-6) = -4`

`a_4 - a_3 = -14 - (-10) = -4`

and so on. It follows that a recursive rule for the sequence might be

`\begin{cases} a_1 = -2 \\ a_n = a_(n-1) - 4 & \text{for } n\ge2 \end{cases}`