Code Breaking

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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 common ratio in a geometric sequence?

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To find the common ratio, divide any term in the sequence by the previous term.

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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, known as 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 term that follows it.

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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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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 next term in the sequence: 2, 4, 8, 16, ...?

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The next term is 32, as this is a geometric sequence with a common ratio of 2.

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What is the next term in the sequence: 10, 7, 4, 1, ...?

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The next term is -2, as this is an arithmetic sequence with a common difference of -3.

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How do you identify a geometric sequence?

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A sequence is geometric if the ratio of consecutive terms is constant.

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How do you identify an arithmetic sequence?

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A sequence is arithmetic if the difference between consecutive terms is constant.