Arithmetic vs Geometric Sequences

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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.

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

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The common difference (d) is found by subtracting any term from the subsequent term: d = a(n) - a(n-1).

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

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The common ratio (r) is found by dividing any term by the previous term: r = a(n) / a(n-1).

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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.

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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).

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What does a(1) represent in a sequence?

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a(1) represents the first term of the sequence.

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If the first term of a geometric sequence is 5 and the common ratio is 2, what is the 4th term?

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The 4th term is a(4) = 5 * 2^(4-1) = 5 * 8 = 40.

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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 a(5) = 10 + (5-1) * 3 = 10 + 12 = 22.

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What is the difference between arithmetic and geometric sequences?

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Arithmetic sequences use addition/subtraction (common difference), while geometric sequences use multiplication/division (common ratio).