Arithmetic and 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?

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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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How do you find 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

How do you find 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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What is the common difference in the sequence: 10, 15, 20, 25, ...?

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The common difference is 5.

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What is the common ratio in the sequence: 2, 6, 18, 54, ...?

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The common ratio is 3.

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Find the 8th term of the arithmetic sequence: 3, 7, 11, 15, ...

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The 8th term is 31.

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Find the 5th term of the geometric sequence: 4, 12, 36, 108, ...

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The 5th term is 324.

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What is the formula for the sum of the first n terms of an arithmetic sequence?

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The formula is S_n = n/2 * (a_1 + a_n), where S_n is the sum of the first n terms, a_1 is the first term, and a_n is the nth term.

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What is the formula for the sum of the first n terms of a geometric sequence?

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The formula is S_n = a_1 * (1 - r^n) / (1 - r), where S_n is the sum of the first n terms, a_1 is the first term, r is the common ratio, and n is the number of terms.