Question

To describe a specific arith-

Answer 1

Answer:

$f(x) = 7x + 30$

Step-by-step 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:

$m = \frac{37 - 30}{1 - 0} = 7$