Vocabulary
Complete the chart.
Word | Definition |
Sequence | ________________________________________________________ |
______________ | a sequence that has a common difference |
______________ | a sequence that has a common ratio |
Explicit formula | ________________________________________________________ |
Recursive formula |
________________________________________________________ |
______________ | a subset of the integers: {1,2,3,4,5....} |
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What is the difference between a recursive formula and an explicit formula?
Recursive Formulas
Using the given recursive formulas, identify the next 5 terms in the sequences that follow:
- and
- and
- and
Given the following sequence of numbers find the recursive formula
- 1, 5, 9, 13, 17
- -1, 3, 2, 5, 7, 12, 19
- -4, 16, -64, 256, -1024
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Explicit Formulas
Given a recursive definition of an arithmetic or geometric sequence, you can always find an explicit formula, or an equation to represent the n th term of the sequence.
What is the equation to find the explicit formula of an arithmetic sequence? ___________________
Geometric sequence? ___________________
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Name the sequence as arithmetic, geometric, or neither.
Write the first 5 terms of the arithmetic sequence(explicit).
Write the formula for the explicit term of the arithmetic sequence.
Convert the explicit and rewrite as recursion:
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