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3 votes
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

User Ionizer
by
6.7k points

1 Answer

3 votes

Answer:


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

User Khanh TO
by
6.3k points