Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference.

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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.

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CCSS.HSF.BF.A.2

Front

Define explicit formula in the context of sequences.

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An explicit formula defines the nth term of a sequence as a function of n, allowing direct computation of any term without needing to know the previous terms.

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CCSS.HSF.BF.A.2

Front

Define recursive formula in the context of sequences.

Back

A recursive formula defines each term of a sequence based on the previous term(s), requiring knowledge of earlier terms to find the next term.

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CCSS.HSF.BF.A.2

Front

What is the common difference in the arithmetic sequence 3, 7, 11, 15, ...?

Back

The common difference is 4.

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CCSS.HSF.BF.A.2

Front

What is the common ratio in the geometric sequence 2, 6, 18, 54, ...?

Back

The common ratio is 3.

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CCSS.HSF.BF.A.2

Front

Write the explicit formula for the arithmetic sequence 5, 10, 15, ...

Back

a_n = 5n.

Tags

CCSS.HSF.BF.A.2

Front

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

Back

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

Tags

CCSS.HSF.BF.A.2

Front

What is the explicit formula for the geometric sequence 4, 12, 36, ...?

Back

a_n = 4 imes 3^{(n-1)}.

Tags

CCSS.HSF.BF.A.2

Front

Write the recursive formula for the geometric sequence 4, 12, 36, ...

Back

a_1 = 4; a_n = a_{n-1} imes 3.

Tags

CCSS.HSF.BF.A.2