Arithmetic and Geometric Sequences 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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How do you find the common difference in an arithmetic sequence?

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To find the common difference, subtract any term from the subsequent term. For example, in the sequence 3, 7, 11, the common difference is 7 - 3 = 4.

Front

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 ratio in a geometric sequence?

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To find the common ratio, divide any term by the previous term. For example, in the sequence 2, 6, 18, the common ratio is 6 / 2 = 3.

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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, d is the common difference, and n is the term number.

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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), where a_1 is the first term, r is the common ratio, and n is the term number.

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Calculate the common difference in the arithmetic sequence: 10, 15, 20, 25.

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The common difference is 5.

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Calculate the common ratio in the geometric sequence: 5, 15, 45, 135.

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The common ratio is 3.

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

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

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

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