arithmetic and geometric sequences

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

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

Back

To find the common difference, subtract the first term from the second term (or any two consecutive terms).

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CCSS.HSF.BF.A.2

Front

Given the arithmetic sequence 13, 19, 25, what are the next two terms?

Back

31 and 37.

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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

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

Back

To find the common ratio, divide any term by the previous term.

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CCSS.HSF.BF.A.2

Front

Write the explicit formula for the nth term of an arithmetic sequence.

Back

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

Write the explicit formula for the nth term of a geometric sequence.

Back

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

Front

What is the common difference of the sequence 2, -1, -4, -7?

Back

-3.

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CCSS.HSF.BF.A.2

Front

Find the common difference for the sequence -34, -29, -24, -19.

Back

5.

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CCSS.HSF.BF.A.2

Front

Given the sequence 125, 25, 5, what is the rule using the geometric sequence formula?

Back

a_n = (125)(1/5)^(n-1).

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CCSS.HSF.BF.A.2