Question

What is the recursive rule for the sequence? −22.7, −18.4, −14.1, −9.8, −5.5, ... an=an+1+4.3 , where a1=−22.7 an=an−1+4.3 , where a1=−22.7 an=an−1−4.3 , where a1=−22.7 an=an+1−4.3 , where a1=−22.7?

Answer 1

This is an arithmetic sequence with common difference 4.3

The rule is an = an-1 + 4.3 where a1 = -22.7

Answer 2

The correct option is 2.

Explanation:

The given sequence is

−22.7, −18.4, −14.1, −9.8, −5.5, ...

Here first term is -22.7. It means

`a_1=-22.7`

The common difference is

`d=a_2-a_1=-18.4-(-22.7)=-18.4+22.7=4.3`

Since we know that

`d=a_n-a_(n-1)`

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

`a_n=a_(n-1)+4.3`

Therefore option 2 is correct.