Arithmetic & Geometric Sequence Practice

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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?

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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.

Front

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 (e.g., d = a2 - a1).

Front

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 (e.g., r = a2 / a1).

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

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The nth term (an) of an arithmetic sequence can be calculated using the formula: an = a1 + (n-1)d, where a1 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 nth term (an) of a geometric sequence can be calculated using the formula: an = a1 * r^(n-1), where a1 is the first term and r is the common ratio.

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If the first term of an arithmetic sequence is 10 and the common difference is 3, what is the 5th term?

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The 5th term is 10 + (5-1) * 3 = 22.

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

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The 4th term is 4 * 2^(4-1) = 32.

Front

What is the common difference of the sequence: 7, 10, 13, 16, ...?

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The common difference is 3.

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What is the common ratio of the sequence: 3, 6, 12, 24, ...?

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The common ratio is 2.