Question

The following function represents an arithmetic sequence.

f(1)=−1.5
f(n+1)=f(n)+0.5
What is f(10)?

Answer 1

3

Explanation:

Each term of the sequence has 0.5 added to the one before. The first 10 terms are ...

-1.5, -1.0, -0.5, 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0

f(10) = 3.0

_____

If you like, you can use the given information about the first term (-1.5) and the common difference (0.5) to write an explicit formula:

f(n) = f(1) +d(n -1)

f(n) = -1.5 +0.5(n -1)

Then the 10th term is ...

f(10) = -1.5 +0.5(10 -1) = -1.5 +4.5 = 3