Question

What is the recursive rule for the sequence?

−2.7, −8.3, −13.9, −19.5, −25.1




an=an+1+5.6, where a1=−2.7

an=an+1−5.6, where a1=−2.7

an=an−1+5.6, where a1=−2.7

an=an−1−5.6, where a1=−2.7

Answer 1

`a_(n) =a_(n-1) -5.6` where
`a_(1) =-2.7`

Explanation:

This is an arithmetic sequence with the first term is
`a_(1)` = -2.7 and has a common difference of
`d=-5.6`.

Arithmetic Sequence:
`a_(n) =a_(n-1) +d`

`a_(n)` is the nth term and
`d` is the common difference.

The common difference: -2.7, -8.3, -13.9...

Subtract: -2.7- (-8.3) = -5.6, -13.9 - (-8.3) = -5.6

Common difference:
`d = -5.6`

Recursive rule:
`a_(n) = a_(n-1) -5.6`