Recursive and Explicit Formulas Worksheet
Explore recursive and explicit formulas for sequences with this Grade 6 math worksheet, including fill-in-the-blanks, multiple choice, and short answer questions.
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Recursive and Explicit Formulas
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Read each question carefully and answer to the best of your ability. Show all your work for short answer questions.
1. A formula defines each term in a sequence using the previous term(s).
2. An formula defines each term in a sequence directly by its position.
3. In the sequence 2, 4, 6, 8, the common is 2.
4. The first term of a sequence is often denoted as .
5. Which of the following is a recursive formula for the sequence 3, 6, 9, 12, ...?
a_n = 3n
a_n = a_{n-1} + 3
a_n = 3 + n
a_n = a_{n-1} * 3
6. For the explicit formula a_n = 2n + 1, what is the 4th term?
5
7
9
11
7. Write the first 5 terms of the sequence defined by the recursive formula: a_1 = 5, a_n = a_{n-1} + 2
8. Write an explicit formula for the sequence: 10, 20, 30, 40, ...
9. A recursive formula is generally easier to use for finding the 100th term of a sequence than an explicit formula.
True
False
10. The sequence defined by a_n = n^2 will always have positive terms.
True
False
11. Consider the sequence: 1, 3, 5, 7, ...
a) What is the next term in the sequence?
b) Write a recursive formula for the sequence.
c) Write an explicit formula for the sequence.