In this lesson, our instructor Vincent Selhorst-Jones teaches Arithmetic Sequences and Series. You will learn about arithmetic sequences, their formulas, and the form for the nth term. Vincent will go over the general formula and how he came to it. Then youll have the chance to practice with five worked-out examples.
A sequence is arithmetic if the difference between any two consecutive terms is constant:
an−an−1 = d,
where d is a constant. We call d the common difference. Every "step" in the sequence has the same change. The difference can be positive or negative, so long as it's always the same.
The formula for the nth term (general term) of an arithmetic sequence is
an = a1 + (n−1)d.
To find the formula for the general term of an arithmetic sequence, we only need to figure out its first term (a1) and the common difference (d).
We can use the following formula to calculate the value of an arithmetic series. Given any arithmetic sequence a1, a2, a3, …, the sum of the first n terms (the nth partial sum) is
·(a1 + an).
We can find the sum by only knowing the first term (a1), the last term (an), and the total number of terms (n). [Caution: Be careful to pay attention to how many terms there are in the series. It can be easy to get the value
of n confused and accidentally think it is 1 higher or 1 lower than it really is.]
Arithmetic Sequences & Series
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.