Geometric and Arithmetic Sequences

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

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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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 in the sequence.

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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 any term from the previous term in the sequence.

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CCSS.HSF.BF.A.2

Front

What is the formula for the nth term of a geometric sequence?

Back

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, r is the common ratio, and n is the term number.

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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 of an arithmetic sequence can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference, and n is the term number.

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio of the geometric sequence -1, 6, -36, 216, ...?

Back

-6

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CCSS.HSF.BF.A.2

Front

What is the 8th term in the geometric sequence 3, 9, 27, 81, ...?

Back

6,561

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CCSS.HSF.BF.A.2

Front

Identify the common difference in the sequence 97, 86, 75, 64, ...

Back

-11

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio of the sequence 5, 25, 125, ...?

Back

5

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CCSS.HSF.BF.A.2