Do Now: 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. For example, in the sequence 3, 6, 9, 12, the common difference is 3.

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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. For example, in the sequence 2, 4, 8, 16, the common ratio is 2.

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How do you find the next term in an arithmetic sequence?

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To find the next term in an arithmetic sequence, add the common difference to the last term. For example, if the sequence is 3, 6, 9, the next term is 9 + 3 = 12.

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How do you find the next term in a geometric sequence?

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To find the next term in a geometric sequence, multiply the last term by the common ratio. For example, if the sequence is 2, 6, 18, the next term is 18 * 3 = 54.

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

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

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What is a common difference in an arithmetic sequence?

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The common difference is the fixed amount that each term increases or decreases by in an arithmetic sequence. For example, in the sequence 5, 10, 15, the common difference is 5.

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What is a common ratio in a geometric sequence?

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The common ratio is the fixed number that each term is multiplied by to get the next term in a geometric sequence. For example, in the sequence 3, 9, 27, the common ratio is 3.

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What is the 7th term of the Fibonacci sequence?

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The Fibonacci sequence starts with 1, 1, 2, 3, 5, 8, 13, ... The 7th term is 13.

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Given the sequence 10, 20, 40, what is the common ratio?

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The common ratio is 2, since each term is multiplied by 2 to get the next term.