Homework Questions

Arithmetic Series

Mrs. Ramsey

Arithmetic Series

A series is the expression for the SUM of the terms in a sequence.

Finite sequences and series have terms you can count individually from 1 to a final whole number, n.

Infinite sequences and series continue without end. (infinity)

Examples

Finite Sequence: 6, 9, 12, 15, 18

Finite Series: 6 + 9 + 12 + 15+ 18

Infinite Sequence: 3, 7, 11, 15…

Infinite Series: 3 + 7 + 11 + 15 +…

Finite Sequence

2, 11, 20, 29, 38, 47Write the related series:

Evaluate the series:

An arithmetic series is a series whose terms form an arithmetic sequence.

Sum of a Finite Arithmetic Series:

a1: 1st terman: nth termn: number of terms

)(2 1 nn aan

S

Example:

Find the sum:1, 3, 5, 7DON’T just add…use the formula

)(2 1 nn aan

S

Summation Notation

3

1

)15(n

n

Write the series in summation notation:

1. 3 + 6 + 9 +…for 33 terms

2. 1 + 2 + 3 + …for n=6

3. 3 + 8 + 13 + 18 +…for n=9

Find the sum of the series:

1.

2.

3.

4.

10

1

)3(n

n

3

1

)15(n

n

4

1

)12

1(

n

n

5

2

2

n

n

Homework

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