Sequences and Series.

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Presentation transcript:

Sequences and Series

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

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

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

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

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

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

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.