1. Sequences and Series

2. Definitions
A sequence is a function whose domain is a set of consecutive integers.
If not specified, it is understood that the domain starts with 1.
Values in the range are called the terms of the sequence.
A series is when the terms of sequence are added together
A series can be finite or infinite (i.e. we can add a finite number of terms or all of the infinite number of terms

3. Arithmetic Sequence Terms have a common difference, denoted by d.
Rule to find the nth term of the sequence:
un=u1+(n-1)d

4. Arithmetic Series
Expression formed by adding the first n terms of an arithmetic sequence.
Will only work for a finite series.

5. Geometric Sequence Terms have a common ratio, denoted by r.
Rule to find the nth term of the sequence:

6. Geometric Series
Expression formed by adding the first n terms of a geometric sequence.

7. Infinite Geometric Series
The sum is called a partial sum. These partial sums may approach a limiting value.
If , then

8. Example
In an arithmetic sequence, the first term is -7 and the sum of the first 20 terms is 620.
1) Find the common difference d.
2) Find the value of the 78th term.