The arithmetic series 15+18+21++84+87 has how many terms?

We can use the general term of the arithmetic series. Look:

Where:

: first term, 15.

: last term, 87.

n: number of terms (what we looking for);

r: reason, which is equal to the difference between two terms, that is, 3.

Let's go to the calculations.

There are 25 terms.

The series has 25 terms.

Step-by-step explanation:

You could just diligently count, but it looks much better if you use the formula for the n-th term of an arithmetic series like this:

so the k=0 term is 15,  k=1 is 18, etc. Now we solve an equation as follows:

so the last term (87) occurs for k=24, which means, including the 0-th term, there are 25 terms in this series.

The advantage of this method is that it would work for very very long series just as nicely, like 15+18+21+...+ 3015, 3018 (where the diligent method would just be way too boring)