Recursive Formulas Worksheet
Grade 10 math worksheet on understanding and applying recursive formulas to sequences.
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Recursive Formulas Worksheet
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Read each question carefully and follow the instructions. Show all your work where applicable.
1. A recursive formula defines each term of a sequence using terms.
2. To define a sequence recursively, you need a starting value (the first term) and a that relates subsequent terms to previous ones.
3. The Fibonacci sequence is a famous example of a sequence defined by a formula.
4. Write the first five terms of the sequence defined by the recursive formula: a₁ = 3, aₙ = aₙ₋₁ + 5 for n > 1.
5. Given the recursive formula: a₁ = 20, aₙ = 0.5 * aₙ₋₁ for n > 1. Find the 4th term of the sequence.
6. Which of the following is the recursive formula for the arithmetic sequence 5, 8, 11, 14, ...?
a₁ = 5, aₙ = aₙ₋₁ + 3
a₁ = 5, aₙ = 3aₙ₋₁
a₁ = 5, aₙ = aₙ₋₁ - 3
a₁ = 5, aₙ = aₙ₋₁ * 3
7. For the sequence 100, 50, 25, 12.5, ..., what is the recursive formula?
a₁ = 100, aₙ = aₙ₋₁ - 50
a₁ = 100, aₙ = aₙ₋₁ / 2
a₁ = 100, aₙ = aₙ₋₁ + 50
a₁ = 100, aₙ = 2aₙ₋₁
8. A recursive formula always requires the first term of the sequence to be explicitly stated.
True
False
9. An explicit formula is generally more useful for finding the 100th term of a sequence than a recursive formula.
True
False
10. Write a recursive formula for the sequence 1, 3, 7, 15, 31, ...