Sequences

Front

What is a sequence?

Back

A sequence is an ordered list of numbers that follow a specific pattern or rule.

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What is an arithmetic sequence?

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An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

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What is the common difference (d) in an arithmetic sequence?

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The common difference (d) is the fixed amount added to each term to get the next term in an arithmetic sequence.

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How do you find the nth term of an arithmetic sequence?

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The nth term (a_n) 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

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

What is the common ratio (r) in a geometric sequence?

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The common ratio (r) is the factor by which we multiply each term to get the next term in a geometric sequence.

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How do you find the nth term of a geometric sequence?

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The nth term (a_n) 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 formula for the sum of the first n terms of an arithmetic sequence?

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

Front

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

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The sum (S_n) of the first n terms can be calculated using the formula: S_n = a_1 * (1 - r^n) / (1 - r) for r ≠ 1.

Front

Given a_1 = 5 and d = 2, find a_6.

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a_6 = 5 + (6-1) * 2 = 15.