Mathematical Patterns and Sequences

Front

What is a mathematical pattern?

Back

A mathematical pattern is a sequence or arrangement of numbers, shapes, or other elements that follow a specific rule or formula.

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What is a sequence in mathematics?

Back

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

Front

What is the next number in the sequence: 2, 4, 6, 8, ...?

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10

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What is the rule for the sequence: 3, 6, 9, 12, ...?

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The rule is to add 3 to the previous number.

Front

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

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The nth term 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 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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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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What is the next term in the sequence: 5, 10, 20, 40, ...?

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80

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How do you identify a pattern in a sequence?

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To identify a pattern, look for a consistent rule that applies to the differences or ratios between consecutive terms.

Front

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

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The formula is 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.