Patterns and Inductive Reasoning (2)
Example 1
Form a conjecture on each pattern of numbers. Then find the next 3 terms.
| 1. |
6, 9, 12, 15, . . .
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| 2. |
–4, 8, –16, 32, . . .
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| 3. |
5, 6, 8, 11, . . .
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Solution
| 1. |
You can form the conjecture by stating that you add the constant 3 to the previous term to get the next term.
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Hence, the next 3 terms in the sequence will be 18, 21, and 24.
The pattern of numbers where each term is obtained by adding a constant to the previous term is called an arithmetic sequence.
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| 2. |
You can arrive at the conjecture that you have to multiply the previous term by the constant –2 to get the next term.
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Hence, the next 3 terms in the sequence will be –64, 128, and –256.
The pattern of numbers where each term is obtained by multiplying the previous term by a constant is called a geometric sequence.
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| 3. |
Observe the numbers that you add to get the next term.
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Form the conjecture by stating that you add the next counting number to the previous term to get the next term. Hence, the next 3 terms in the sequence will be 15, 20, and 26.
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