Instructions: For the following sequence, state the common ratio, identify which is the explicit form and which is the recursive form of the rule, and find the term listed.Sequence: 3,6,12,24…3,6,12,24…Find: a9𝑎9Common Ratio: Answer 1 Question 2an=3⋅(2)n−1𝑎𝑛=3⋅(2)𝑛−1Answer 2 Question 2an=an−1⋅2𝑎𝑛=𝑎𝑛−1⋅2a1=3𝑎1=3Answer 3 Question 2a9=𝑎9= Answer 4 Question 2
Question
Instructions: For the following sequence, state the common ratio, identify which is the explicit form and which is the recursive form of the rule, and find the term listed.Sequence: 3,6,12,24…3,6,12,24…Find: a9𝑎9Common Ratio: Answer 1 Question 2an=3⋅(2)n−1𝑎𝑛=3⋅(2)𝑛−1Answer 2 Question 2an=an−1⋅2𝑎𝑛=𝑎𝑛−1⋅2a1=3𝑎1=3Answer 3 Question 2a9=𝑎9= Answer 4 Question 2
Solution
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The common ratio of the sequence is 2. This is because each term is twice the previous term (6 is twice 3, 12 is twice 6, 24 is twice 12, etc.).
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The explicit form of the rule is an=3⋅(2)n−1. This is because each term an can be found directly by multiplying 3 by 2 raised to the power of (n-1), where n is the term number.
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The recursive form of the rule is an=an−1⋅2, a1=3. This is because each term an is found by multiplying the previous term an-1 by 2, with the first term a1 being 3.
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To find the 9th term a9, we can use the explicit form of the rule: a9=3⋅(2)9−1 = 3 * 2^8 = 3 * 256 = 768. So, a9 = 768.
Similar Questions
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