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: a n = n (plug in 1, 2, 3, 4, 5) 1, 2, 3, 4, 5

More Examples 1. a n = 4n 2. a n = 2n-3 3. a n = |1-n 2 | 4. a n = 5. a n =

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, …} a n = n + 7

Examples of Explicit {-3, 1, 5, 9, …} {1, 4, 9, 16, …} {7, 9, 11, 13, …} {24, 20, 16, 12, …}

Arithmetic Sequences

In an arithmetic sequence, the difference between consecutive terms is constant. The difference is called the common difference. To find d: 2 nd term – 1 st term

Arithmetic? 1. 2, 4, 8, , 12, , 45, , 5, 7, 12

Arithmetic Sequence Formulas Recursive Formula a n = a n-1 + d use if you know prior terms Explicit Formula a n = a 1 + (n-1)d a n = nth term a 1 = 1 st term n = number of terms d = common difference

Examples Find the 20 th term of each sequence , 201, 189, 177… ,.0025,.0027…

More examples Find the 17 th term of the sequence: 3. a 16 = 18, d = 5

Find the missing term Use arithmetic mean = average! 4. 84, _______, , _______, 57

Geometric Sequences

In a geometric sequence, the ratio between consecutive terms is constant. This ratio is called the common ratio. To find r:

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 a n = a n-1 r Explicit Formula a n = a 1 r n-1

Find the 19 th 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, _____, , ____, 18, , ____, 5103

Homework WORKSHEET! We need to talk about numbers though, so wait on me!