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.

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CCSS.HSF.BF.A.2

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What is the common difference 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.

Tags

CCSS.HSF.BF.A.2

Front

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

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The nth term (a_n) of an arithmetic sequence 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.

Tags

CCSS.HSF.BF.A.2

Front

What is a geometric sequence?

Back

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.

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio 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.

Tags

CCSS.HSF.BF.A.2

Front

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

Back

The nth term (a_n) 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.

Tags

CCSS.HSF.BF.A.2

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What is a recursive formula?

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A recursive formula defines each term of a sequence using the preceding term(s).

Tags

CCSS.HSF.BF.A.2

Front

Write the recursive formula for the arithmetic sequence 5, 10, 15, 20...

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a_n = a_{n-1} + 5, a_1 = 5.

Tags

CCSS.HSF.BF.A.2

Front

What is the explicit formula for the arithmetic sequence 2, 5, 8, 11...?

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a_n = 2 + (n-1) * 3.

Tags

CCSS.HSF.BF.A.2

Front

What is the explicit formula for the geometric sequence 3, 6, 12, 24...?

Back

a_n = 3 * 2^(n-1).

Tags

CCSS.HSF.BF.A.2