Arithmetic, Geometric Sequences, Explicit, Recursive Formula

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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. For example, 2, 4, 6, 8 is an arithmetic sequence with a common difference of 2.

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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. For example, 3, 6, 12, 24 is a geometric sequence with a common ratio of 2.

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What is the explicit formula for an arithmetic sequence?

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The explicit formula for an arithmetic sequence is given by a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference.

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What is the recursive formula for an arithmetic sequence?

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The recursive formula for an arithmetic sequence is a_n = a_(n-1) + d, where a_n is the nth term, a_(n-1) is the previous term, and d is the common difference.

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What is the explicit formula for a geometric sequence?

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The explicit formula for a geometric sequence is given by a_n = a_1 * r^(n-1), where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the term number.

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What is the recursive formula for a geometric sequence?

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The recursive formula for a geometric sequence is a_n = a_(n-1) * r, where a_n is the nth term, a_(n-1) is the previous term, and r is the common ratio.

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How do you find the common difference in an arithmetic sequence?

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The common difference (d) in an arithmetic sequence can be found by subtracting any term from the subsequent term. For example, in the sequence 5, 8, 11, the common difference is 8 - 5 = 3.

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How do you find the common ratio in a geometric sequence?

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The common ratio (r) in a geometric sequence can be found by dividing 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 are the next 3 terms in the arithmetic sequence: 3, 7, 11, 15?

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The next 3 terms are 19, 23, 27.

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What is the 15th term of the sequence a_n = -3n + 50?

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The 15th term is 5.