Number Patterns and Algebraic Rules
Name: _______________________________
Date: _______________________________
Part A: Continue the Pattern
Write the next three terms in each sequence.
1.
3, 7, 11, 15, _______, _______, _______
2.
20, 17, 14, 11, _______, _______, _______
3.
5, 12, 19, 26, _______, _______, _______
4.
50, 45, 40, 35, _______, _______, _______
Part B: Describe the Rule
Describe the rule for each pattern in words.
5. Pattern: 4, 9, 14, 19, 24...
Rule: _________________________________________________________
6. Pattern: 100, 92, 84, 76, 68...
Rule: _________________________________________________________
Part C: Find the nth Term
Find the algebraic rule for the nth term of each sequence.
7. Sequence: 5, 10, 15, 20, 25...
nth term = _____________________
8. Sequence: 7, 9, 11, 13, 15...
nth term = _____________________
9. Sequence: 1, 4, 7, 10, 13...
nth term = _____________________
10. Sequence: 12, 22, 32, 42, 52...
nth term = _____________________
Part D: Apply the Rule
Use the given rule to find the requested term.
11. If the nth term is 4n + 1, find the 10th term.
Answer: _____________________
12. If the nth term is 6n - 2, find the 8th term.
Answer: _____________________
13. If the nth term is 50 - 3n, find the 12th term.
Answer: _____________________
Part E: Challenge Questions
14. A pattern starts at 8 and increases by 6 each time. What is the 20th term?
Answer: _____________________
15. The nth term of a sequence is 2n + 5. Which term has a value of 35?
Answer: The __________ term