Precalculus · Grades 10 to 12
Sequences and series
Find a term and add up the first n terms.
The idea
An arithmetic sequence adds the same number each time. That number is the common difference.
A geometric series multiplies each term by the same number. The sum of the first n terms has the formula S = a(r^n - 1) / (r - 1).
Worked examples
- How to Find the nth Term of an Arithmetic Sequence Find the 10th term of 3, 7, 11, 15. Four steps with the common difference and the formula, and the off-by-one mistakes to avoid.
- How to Find the Sum of a Geometric Series Add 2 + 6 + 18 + 54 + 162 with the geometric series formula. Four steps, the ratio, the r - 1 mistakes to avoid and practice answers.
- How to Find the Sum of an Arithmetic Series Add the first 20 terms of 3, 7, 11, ... with S = n/2(2a + (n-1)d). Four steps that find a and d first, and the count mistakes to avoid.
Practice this topic
3 problems with answers.