Question

The 3rd term of an arithmetic sequence

is −2, and the 8th term is −32. Write a function to describe this sequence

Answer 1

Explanation:

Arithmetic sequence have a common difference so we need to find the common difference.

Formula for a arithmetic sequence is

`y = a + (n - 1)d`

The 8th term is -32 and the third

term is -2

We need to find average rate of change so we just do

`( - 32 - ( - 2))/(5) = ( - 30)/(5) = - 6`

So the average rate of change is -6 so we have

`a +( - 6 )(n - 1) =`

We need to find the initial value, let just subtract -6 from -2 twice.

`- 2 - ( - 6) - ( - 6) = 10`

So our inital value is 10

`10 + ( - 6)(n - 1)`