Recursive Formulas Worksheet
This worksheet focuses on understanding and applying recursive formulas for sequences, including arithmetic and geometric sequences, and solving problems involving recurrence relations.
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Recursive Formulas
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. Given the recursive formula a_n = a_(n-1) + 5, with a_1 = 3, find the first five terms of the sequence.
2. Which of the following recursive formulas represents a geometric sequence?
a_n = a_(n-1) + 2
a_n = 3 * a_(n-1)
a_n = a_(n-1) - n
a_n = (a_(n-1))^2
3. For an arithmetic sequence with a_1 = 7 and a common difference of -4, the recursive formula is a_n = and a_1 = .
4. Write a recursive formula for the sequence: 10, 20, 40, 80, ...
5. A recursive formula always requires the previous term(s) to find the next term.
True
False
6. A bank account starts with $1000. Each year, 5% interest is added to the balance. Write a recursive formula for the amount of money in the account at the end of 'n' years.
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