# Arithmetic Sequences and Series

## Presentation on theme: "Arithmetic Sequences and Series"— Presentation transcript:

Arithmetic Sequences and Series

Arithmetic Sequences

An Arithmetic Sequence is defined as a sequence in which there is a common difference between consecutive terms.

Which of the following sequences are arithmetic
Which of the following sequences are arithmetic? Identify the common difference. YES YES NO NO YES

The common difference is always the difference between any term and the term that proceeds that term. Common Difference = 5

The general form of an ARITHMETIC sequence.
First Term: Second Term: Third Term: Fourth Term: Fifth Term: nth Term:

Formula for the nth term of an ARITHMETIC sequence.
If we know any three of these we ought to be able to find the fourth.

Given: Find: IDENTIFY SOLVE

Find: What term number is -169?
Given: Find: What term number is -169? IDENTIFY SOLVE

Given: Find: What’s the real question? The Difference IDENTIFY SOLVE

Given: Find: IDENTIFY SOLVE

Arithmetic Series

Write the first three terms and the last two terms of the following arithmetic series.
What is the sum of this series?

What is the SUM of these terms?
Written 1st to last. Written last to 1st. Add Down 50 Terms 71 + (-27) Each sum is the same.

In General . . .

Find the sum of the terms of this arithmetic series.

Find the sum of the terms of this arithmetic series.
What term is -5?

Alternate formula for the sum of an Arithmetic Series.

Find the sum of this series
It is not convenient to find the last term.