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Student Task Statement
Pattern A: De ne the sequence so that is the number of white squares in stage , and de ne the sequence so that is the number of black squares in stage .
1. Find a recursive or closed form de nition for sequence .
2. Find a recursive or closed form de nition for sequence .
3. Are they arithmetic, geometric, or neither? Explain how you know.
Pattern B: The table shows two animal populations growing over time.
time, years since 1990
Population 1
Population 2
0
23,000
3,125
1
29,000
3,750
2
35,000
4,500
3
41,000
5,400
4
47,000
6,480
1. Find a recursive or closed form de nition for Population 1.
2. Find a recursive or closed form de nition for Population 2.
3. Are they arithmetic, geometric, or neither? Explain how you know.
4. Did Population 2 ever overtake Population 1? If so, when? Explain how you know.
Student Response
Pattern A:
1. Sample responses: for ; (or equivalent)
2. Sample responses: for ; (or equivalent)
3. Sample response: is an arithmetic sequence, because the same number is added each time to get from one term to the next. is neither geometric nor arithmetic, because its terms
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Teacher Guide Algebra