Arithmetic Sequences and Common Differences

Front

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

Front

What is the common difference in an arithmetic sequence?

Back

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

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CCSS.HSF.BF.A.2

Front

How do you find the common difference in the sequence: 29, 21, 13, 5, ...?

Back

The common difference is d = -8.

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CCSS.HSF.BF.A.2

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The nth term (a_n) 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.

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CCSS.HSF.BF.A.2

Front

Find the 32nd term of the sequence: 34, 37, 40, 43, ...

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The 32nd term is 127.

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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.

Tags

CCSS.HSF.BF.A.2

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How do you find the common ratio in the sequence: 64, -16, 4, -1, ...?

Back

The common ratio is r = -1/4.

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CCSS.HSF.BF.A.2

Front

Determine if the sequence 2, 5, 8, 11, 14, ... is arithmetic or geometric.

Back

The sequence is arithmetic.

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CCSS.HSF.BF.A.2

Front

What is the difference between an arithmetic sequence and a geometric sequence?

Back

An arithmetic sequence has a constant difference between terms, while a geometric sequence has a constant ratio between terms.

Tags

CCSS.HSF.BF.A.2

Front

If the first term of an arithmetic sequence is 10 and the common difference is 3, what is the 5th term?

Back

The 5th term is 22.

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CCSS.HSF.BF.A.2