Question

To describe a specific arith-

metic sequence, Elijah wrote
the recursive formula:
[ f(0) = 30
f(n+1)=f(n)+7
Write a linear equation that
models this sequence

Answer 1

`f(x) = 7x + 30`

Explanation:

We need at least two points to write the equation of a straight line.

The recursive formula that Elijah wrote is:

`f(0) = 30`

`f(n + 1) = f(n) + 7`

When we substitute n=0, we get:

`f(0 + 1) = f(0) + 7`

`f(1) = 30 + 7`

`f(1) = 37`

The points (0,30) and (1,37) lies on this line.

The equation of this line is of the form:

`f(x) = mx + b`

where b =30 is the y-intercept and m=7 is the slope.

We plug in these values to get:

`f(x) = 7x + 30`

Note that the slope of the line is equal to the common difference of the Arithmetic Sequence.

You could also use the two points to find the slope:

`m = (37 - 30)/(1 - 0) = 7`