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 Examples1. an = 4n

2. an = 2n-3

3. an = |1-n2|

4. an =

5. an = 3

1n

36n

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

sequence1. 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

Geometric Sequences

Geometric Sequences In a geometric sequence, the ratio

between consecutive terms is constant.

This ratio is called the common ratio.

To find r: sttermndterm12

Geometric, Arithmetic, Neither?(find the next 2 terms if so)1. 5, 15, 45, 135…

2. 15, 30, 45, 60…

3. 6, -24, 96, -384…

4. 8, 20, 32, 44…

Geometric Sequences Formulas

Recursive Formula an = an-1 r

Explicit Formula an = a1 rn-1

Find the 19th term…1. 11, 33, 99, 297…

2. 20, 17, 14, 11, 8…

FYI - Graphs Arithmetic Graphs are linear

Geometric Graphs are exponential

Geometric Mean Geometric Mean =

3. 20, _____, 80

4. 3, ____, 18, 75

5. 28, ____, 5103

numbersproductof 2

Homework WORKSHEET! We need to talk about numbers

16-20 though, so wait on me!