Warm -up Suppose angle A is acute and. Find sin2A and cos 2A.

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Presentation transcript:

Warm -up Suppose angle A is acute and. Find sin2A and cos 2A.

SEQUENCES AND SERIES Chapter 13 Identify arithmetic or geometric sequence. Find a formula for a sequence nth term.

What is a sequence? Set of numbers (called terms) that are arranged in a particular order. The set of positive odd integers The set of positive odd integers The set of positive multiples of 3 The set of positive multiples of 3

What is a series? A series is an indicated sum of the terms of a sequence of numbers. The sum of the cubes of the first twenty positive integers. The sum of the cubes of the first twenty positive integers. The sum of the first 100 positive odd integers The sum of the first 100 positive odd integers

There are two special types of sequences: Arithmetic – constant difference The difference between any two consecutive terms is equal-----Constant Difference Geometric – constant ratio The ratio of any two consecutive terms is constant---- Constant Ratio

Arithmetic or Geometric? Is there a common difference or a common ratio?

EXAMPLE OF NOTATION t 1 – First term t 2 – Second term t n – nth term

Arithmetic Sequence Formula Geometric Sequence Formula

Identify the sequence as arithmetic, geometric or neither. Find the nth term.

A sequence of numbers is defined as the positive multiples of 3. What is the 105 th term?

Graphing 3, 5, 7, …. The graph of this sequence only represents discrete points…specific set. Find the formula for the nth term and then sketch the graph of the sequence.

Graphing 3, 4.5, 6.75, …. The graph of this sequence only represents discrete points…specific set. Find the formula for the nth term and then sketch the graph of the sequence.

Homework P odd.

Warm-up Find the exact value of using a sum/difference formula.

Arithmetic and Geometric Sequences Day 2 Finding a sequence given 2 terms.

Finding a term In a geometric sequence, t 3 =12 and t 6 =96. Find t 11

In a sequence, the second term is 2 and the 5 th term is 16. Find the tenth term if the sequence is a) arithmetic b) geometric

Find the number of multiples of 6 between 28 and 280.

How many 4 digit numbers are not divisible by 11?

Given the sequence: a)Find x if the sequence is Arithmetic Geometric

Homework Day P odd Day P , 49, 50