Recursive Formulas Worksheet
This worksheet focuses on understanding and applying recursive formulas for sequences, including arithmetic and geometric sequences, at a Grade 11 level.
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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. Define a recursive formula in your own words, and explain its key components.
2. A sequence where each term after the first is found by adding a constant to the previous term is called an sequence.
3. A sequence where each term after the first is found by multiplying the previous term by a constant is called a sequence.
4. Which of the following recursive formulas represents the sequence 3, 7, 11, 15, ...?
a₁ = 3; aₙ = aₙ₋₁ + 3
a₁ = 3; aₙ = aₙ₋₁ + 4
a₁ = 3; aₙ = 4aₙ₋₁
a₁ = 3; aₙ = aₙ₋₁ - 4
5. Given the recursive formula a₁ = 5; aₙ = 2aₙ₋₁ + 1, what is the third term of the sequence?
11
23
27
55
6. Write the first five terms of the sequence defined by a₁ = -2; aₙ = 3aₙ₋₁ + 5.
7. A population of bacteria doubles every hour. If the initial population is 50, write a recursive formula to represent the population after 'n' hours. Then, find the population after 4 hours.
8. Every arithmetic sequence can be represented by a recursive formula.
True
False