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# Arithmetic Series & Sequence

Algebra 2 Chapter 11

by

Tweet## Melissa Ratliff

on 18 August 2011#### Transcript of Arithmetic Series & Sequence

Sequence & Series The Sum of All Things Do you see a Pattern? GEOMETRIC ARITHMETIC General Term DON'T FORGET TO USEA LITTLE LOGIC Give it a try! 27 + 12x An arithmetic sequence is a

sequence in which each term

after the first is found by

adding a constant. The constant is called

the common difference. nth Term Take a look at

it like this: Example 1

Find the next four terms in the arithmetic sequence

-8, -6, -4, ... What is the common difference? We add 2, so the common difference is 2.

So the next 4 terms are:

-2, 0, 2, 4 Look closer... We need a formula for the general term.

Example 2

Write an equation for the nth term of the sequence -8, -6, -4, ... Arithmetic Means The terms between any two nonsuccessive terms of an arithmetic sequence are called the arithmetic means. Example 3

Find the three arithmetic means between 21 and 45. In other words, just fill in the blanks in the sequence

21, __, __, __, 45. So the three arithmetic means are

27, 33, 39. Find the three arithmetic means between 44 and 92. Example 4

68 is the ___th term in the arithmetic sequence -2, 3, 8, ... . Arithmetic Series You already know alot! Except for the sum formula. Example 5

Find the sum of the first 100 integers. Don't Forget

Sigma

Full transcriptsequence in which each term

after the first is found by

adding a constant. The constant is called

the common difference. nth Term Take a look at

it like this: Example 1

Find the next four terms in the arithmetic sequence

-8, -6, -4, ... What is the common difference? We add 2, so the common difference is 2.

So the next 4 terms are:

-2, 0, 2, 4 Look closer... We need a formula for the general term.

Example 2

Write an equation for the nth term of the sequence -8, -6, -4, ... Arithmetic Means The terms between any two nonsuccessive terms of an arithmetic sequence are called the arithmetic means. Example 3

Find the three arithmetic means between 21 and 45. In other words, just fill in the blanks in the sequence

21, __, __, __, 45. So the three arithmetic means are

27, 33, 39. Find the three arithmetic means between 44 and 92. Example 4

68 is the ___th term in the arithmetic sequence -2, 3, 8, ... . Arithmetic Series You already know alot! Except for the sum formula. Example 5

Find the sum of the first 100 integers. Don't Forget

Sigma