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

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 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 and d is the common difference.

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CCSS.HSF.BF.A.2

Front

How do you find 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 and r is the common ratio.

Tags

CCSS.HSF.BF.A.2

Front

What is the common difference in the sequence 2, 5, 8, 11, ...?

Back

The common difference is 3, as each term increases by 3.

Tags

CCSS.HSF.BF.A.2

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What is the common ratio in the sequence 3, 6, 12, 24, ...?

Back

The common ratio is 2, as each term is multiplied by 2 to get the next term.

Tags

CCSS.HSF.BF.A.2

Front

Find the 5th term of the arithmetic sequence: 4, 9, 14, ...

Back

The 5th term is 24.

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CCSS.HSF.BF.A.2

Front

Find the 4th term of the geometric sequence: 5, 15, 45, ...

Back

The 4th term is 135.

Tags

CCSS.HSF.BF.A.2

Front

What are the next three terms in the arithmetic sequence: 10, 15, 20, ...?

Back

The next three terms are 25, 30, 35.

Tags

CCSS.HSF.BF.A.2

Front

What are the next three terms in the geometric sequence: 2, 6, 18, ...?

Back

The next three terms are 54, 162, 486.

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CCSS.HSF.BF.A.2