Arithmetic & Geometric Sequence Final Review

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What is an arithmetic sequence?

Back

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?

Back

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.

Front

How do you determine if a sequence is arithmetic or geometric?

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To determine if a sequence is arithmetic, check if the difference between consecutive terms is constant. For geometric sequences, check if the ratio of consecutive terms is constant.

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

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The nth term of an arithmetic sequence can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

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

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The nth term of a geometric sequence can be found using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

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Identify the common difference in the sequence: 3, 7, 11, 15,...

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The common difference is 4.

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Identify the common ratio in the sequence: 2, 6, 18, 54,...

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The common ratio is 3.

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What is the 5th term of the arithmetic sequence: 2, 5, 8, 11,...?

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The 5th term is 14.

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What is the 4th term of the geometric sequence: 3, 9, 27, ...?

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The 4th term is 81.

Front

Which sequence is NOT an arithmetic sequence? -7, -13, -19, -25,...; -10, -6, -2, 2; 6, 8, 10, 12; 3, 15, 75, 375,...

Back

3, 15, 75, 375,... is NOT an arithmetic sequence.