Sequences

Front

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 (d).

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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.

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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 (r).

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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.

Front

What is the common difference in the arithmetic sequence 5, 8, 11, 14?

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The common difference (d) is 3, as each term increases by 3.

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

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The common ratio (r) is 3, as each term is multiplied by 3 to get the next term.

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Determine if the sequence 1, 4, 9, 16, ... is arithmetic or geometric.

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The sequence is neither arithmetic nor geometric; it is a sequence of perfect squares.

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What is the next term in the arithmetic sequence 10, 15, 20, ...?

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The next term is 25, as the common difference is 5.

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Identify the type of sequence: 3, 6, 12, 24, ...

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This is a geometric sequence with a common ratio of 2.

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What are the first five terms of the arithmetic sequence defined by f(n) = 2n + 3?

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The first five terms are 5, 7, 9, 11, 13.