You’ve already seen arithmetic (adding/subtracting) and geometric (multiplying/dividing)
sequences, where the question usually asks you for the nth term. Some questions on the test may
ask you to work with a series, which results in a sum of the terms of a sequence. The formula for the
sum of the first n terms of an arithmetic series is
where a 1 is the first term and an is the nth term. Here’s an example:
If the first term in an arithmetic series is 3, and the 10th term is 38, what is the sum of the first 10
terms?
Just plug into the formula the information from the question: n = 10, a 1 = 3, and an = a 10 = 38.
The formula for the sum of the first n terms of a geometric series is
where a term should be a 1 is the first term and r is the common ratio.
There is another way of expressing sums of terms. The ∑ symbol is used to indicate summation, as
in the following example: