Arithmetic and Geometric Sequences

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What is an arithmetic sequence?

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An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference.

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What is a geometric sequence?

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A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

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What is the formula for the nth term of an arithmetic sequence?

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The formula for the nth term of an arithmetic sequence is t_n = a + (n-1)d, where 'a' is the first term and 'd' is the common difference.

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What is the formula for the nth term of a geometric sequence?

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The formula for the nth term of a geometric sequence is t_n = a * r^(n-1), where 'a' is the first term and 'r' is the common ratio.

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CCSS.HSF.BF.A.2

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How do you find the common difference in an arithmetic sequence?

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The common difference can be found by subtracting any term from the subsequent term, i.e., d = t_(n+1) - t_n.

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How do you find the common ratio in a geometric sequence?

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The common ratio can be found by dividing any term by the previous term, i.e., r = t_(n+1) / t_n.

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CCSS.HSF.BF.A.2

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What is the next term in the arithmetic sequence 5, 10, 15, ...?

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The next term is 20.

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What is the next term in the geometric sequence 3, 6, 12, ...?

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The next term is 24.

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If the first term of an arithmetic sequence is 4 and the common difference is 3, what is the 5th term?

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The 5th term is 4 + 4*3 = 16.

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CCSS.HSF.BF.A.2

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If the first term of a geometric sequence is 2 and the common ratio is 3, what is the 4th term?

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The 4th term is 2 * 3^(4-1) = 54.

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