Homework Questions

Number Patterns

Find the next two terms, state a rule to describe the pattern.

1. 1, 3, 5, 7, 9…2. 16, 32, 64…3. 50, 45, 40, 35…4. -3, -7, -11, -15…

Sequence Notation

A sequence is an ordered list of numbers – each number is a term.

State the first 5 terms: an = n (plug in 1, 2, 3, 4, 5) 1, 2, 3, 4, 5

More Examples

1. an = 4n

2. an = 2n-3

3. an = |1-n2|

4. an =

5. an = 3

1

n

3

6n

Recursive v. Explicit

Definition Recursive Formula – a sequence is

recursively defined if the first term is given and there is a method of determining the nth tem by using the terms that precede it.

English – if you can use the term before it to figure out what comes next

Ex: {-7, -4, -1, 2, 5, …}

Examples of Recursive

{-9, -4, -2, 0, 2, …}

{-4, -8, -16, -32, -64, …}

{6, 11, 16, 21, 26, …}

{8, 4, 2, 1, …}

Definition

Explicit Formula – a formula that allows direct computation for any term for a sequence

English – you don’t need to term prior in order to figure out what the nth term is going to be.

Ex: {8, 9, 10, 11, 12, …} an= n + 7

Examples of Explicit

{-3, 1, 5, 9, …}

{1, 4, 9, 16, …}

{7, 9, 11, 13, …}

{24, 20, 16, 12, …}

Arithmetic Sequences

Arithmetic Sequences

In an arithmetic sequence, the difference between consecutive terms is constant.

The difference is called the common difference.

To find d: 2nd term – 1st term

Arithmetic?

1. 2, 4, 8, 16

2. 6, 12, 18

3. 48, 45, 42

4. 2, 5, 7, 12

Arithmetic Sequence Formulas Recursive

Formula an = an-1 + d use if you know

prior terms Explicit Formula

an = a1 + (n-1)d

an = nth term a1 = 1st term n = number of

terms d = common

difference

Examples

Find the 20th term of each sequence

1. 213, 201, 189, 177…

2. .0023, .0025, .0027…

More examples

Find the 17th term of the sequence:

3. a16 = 18, d = 5

Find the missing term

Use arithmetic mean = average!4. 84, _______, 110

5. 24, _______, 57

Homework

WORKSHEET! We need to talk about numbers 16-

20 though, so wait on me!