Test Your Knowledge: Determining the Rule for Math Tables

📚 Quick Study Guide

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• Arithmetic Sequence: A sequence where the difference between consecutive terms is constant. Formula: $a_n = a_1 + (n-1)d$, where $a_n$ is the nth term, $a_1$ is the first term, and $d$ is the common difference.
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• Geometric Sequence: A sequence where each term is multiplied by a constant to get the next term. Formula: $a_n = a_1 * r^{(n-1)}$, where $r$ is the common ratio.
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• Identifying the Rule: Look for patterns by examining the differences or ratios between consecutive numbers in the table. Is it addition, subtraction, multiplication, division, or a combination?
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• Tips for Success: Calculate the differences between terms. If the differences are constant, it's an arithmetic sequence. If the ratios are constant, it's a geometric sequence. If neither, look for more complex polynomial or exponential relationships.
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• General Term: Once you identify a pattern, express the general term, $a_n$, as a function of $n$, which represents the position of the number in the table.

Practice Quiz

1. Which of the following describes an arithmetic sequence?
   1. A) Each term is multiplied by a constant.
   2. B) The difference between consecutive terms is constant.
   3. C) The ratio between consecutive terms is constant.
   4. D) The terms increase exponentially.
2. What is the common difference in the arithmetic sequence: 2, 5, 8, 11, ...?
   1. A) 2
   2. B) 3
   3. C) 4
   4. D) 5
3. What is the common ratio in the geometric sequence: 3, 6, 12, 24, ...?
   1. A) 1
   2. B) 2
   3. C) 3
   4. D) 4
4. What is the next number in the sequence: 1, 4, 9, 16, ...?
   1. A) 20
   2. B) 25
   3. C) 30
   4. D) 36
5. If a table follows the rule $a_n = 3n - 1$, what is the 5th term in the table?
   1. A) 10
   2. B) 12
   3. C) 14
   4. D) 16
6. Which of the following sequences is neither arithmetic nor geometric?
   1. A) 2, 4, 6, 8, ...
   2. B) 1, 3, 9, 27, ...
   3. C) 1, 4, 7, 10, ...
   4. D) 1, 4, 9, 16, ...
7. A table shows the following values: (1, 2), (2, 4), (3, 6), (4, 8). What is the general rule?
   1. A) $a_n = n + 1$
   2. B) $a_n = 2n$
   3. C) $a_n = 3n - 1$
   4. D) $a_n = n^2$