Arithmetic, Geometric Sequences, Explicit, Recursive Formula

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What is an arithmetic sequence?

Back

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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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 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_1 is the first term 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 given by a_n = a_(n-1) + d, where d is the common difference.

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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 an arithmetic sequence?

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The common difference is the fixed amount that each term increases or decreases by in an arithmetic sequence.

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What is the common ratio in a geometric sequence?

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The common ratio is the fixed number that each term is multiplied by to get the next term in a geometric sequence.

Front

Given the sequence 4, 11, 18, 25, what is a_3?

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a_3 = 18.

Front

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

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The 15th term is 5.

Front

Determine the first 3 terms of the sequence defined by t_1 = -3 and t_n = t_(n-1) * 3.

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The first 3 terms are -3, -9, -27.