Grade 9 Recursive Formulas Worksheet
This worksheet focuses on understanding and applying recursive formulas for sequences, suitable for Grade 9 math students.
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Recursive Formulas Worksheet
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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 what a recursive formula is in your own words, and explain how it differs from an explicit formula for a sequence.
2. Given the recursive formula a_n = a_(n-1) + 3, with a_1 = 5, the first five terms of the sequence are: , , , , .
3. For the recursive formula f(n) = 2 * f(n-1), with f(1) = 3, the third term, f(3), is .
4. Which of the following recursive formulas describes an arithmetic sequence with a common difference of -4 and a first term of 10?
a_n = a_(n-1) + 4, a_1 = 10
a_n = a_(n-1) - 4, a_1 = 10
a_n = 4 * a_(n-1), a_1 = 10
a_n = -4 * a_(n-1), a_1 = 10
5. Write a recursive formula for the sequence: 2, 6, 18, 54, ...
6. A savings account starts with $1000 and earns 2% interest compounded annually. Write a recursive formula for the amount of money in the account at the end of 'n' years.
7. A recursive formula always requires the previous term(s) to calculate the next term.
True
False
8. The Fibonacci sequence is defined by F(n) = F(n-1) + F(n-2) with F(1) = 1 and F(2) = 1. Find the first 7 terms of the Fibonacci sequence.