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Homework Questions Number Patterns 1. 2. 3. 4. Find the next two terms, state a rule to describe the pattern. 1, 3, 5, 7, 9… 16, 32, 64… 50, 45, 40, 35… -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. 2. an = 4n 4. 6 3 an = 2n-3 5. 3. an = n an = |1-n2| an = 13 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, …} 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 1. Find the 20th term of each sequence 213, 201, 189, 177… 2. .0023, .0025, .0027… More examples 3. Find the 17th term of the sequence: a16 = 18, d = 5 Find the missing term 4. Use arithmetic mean = average! 84, _______, 110 5. 24, _______, 57 Homework WORKSHEET! We need to talk about numbers 16-20 though, so wait on me!