Question

This arithmetic sequence is defined by the function f(n).

9, 13, 17, 21, 25, ...

What is the y-intercept of this function?

Answer 1

y = 5

Explanation:

The first term (a1) is 9, and the common difference (d) is 4. Then the general term is ...

an = a1 + (n-1)·d = 9 + 4(n -1) = 4n +5

The "y-intercept" corresponds to the value when n=0. That value is ...

a0 = 4·0 +5 = 5

The y-intercept is 5.

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Comment on the problem

We have computed f(n) for n=0, but we must realize that n=0 is outside the domain of the function. This function only makes sense for integer values of n that are greater than zero. The "real" answer is that the y-intercept is "undefined."