Recursive Formulas Worksheet
Explore recursive formulas for sequences, identifying patterns and calculating terms.
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Recursive Formulas Worksheet
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Read each question carefully and follow the instructions to determine the terms of the sequences or identify the recursive formula.
1. A recursive formula defines each term of a sequence using one or more of the terms.
2. For a recursive formula, you always need to know the first of the sequence.
3. In the formula a_n = a_(n-1) + 5, a_(n-1) represents the term.
4. Given the recursive formula a_n = a_(n-1) + 3 and a_1 = 2, find the first 5 terms of the sequence.
5. Given the recursive formula a_n = 2 * a_(n-1) and a_1 = 1, find the first 4 terms of the sequence.
6. Which of the following is a recursive formula for the sequence: 5, 10, 15, 20, ...?
a_n = a_(n-1) + 5
a_n = 5n
a_n = a_(n-1) - 5
a_n = a_(n-1) * 5
7. The sequence 1, 3, 7, 15, ... can be represented by the recursive formula a_n = 2 * a_(n-1) + 1, with a_1 = 1.
True
False
8. Write a recursive formula for the sequence: 100, 50, 25, 12.5, ... and find the 5th term.
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