Arithmetic and Geometric Sequences Review

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. For example, 2, 4, 6, 8 is an arithmetic sequence with a common difference of 2.

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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. For example, 3, 6, 12, 24 is a geometric sequence with a common ratio of 2.

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CCSS.HSF.BF.A.2

Front

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

Back

The common difference in an arithmetic sequence can be found by subtracting any term from the term that follows it. For example, in the sequence 5, 8, 11, the common difference is 8 - 5 = 3.

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CCSS.HSF.BF.A.2

Front

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

Back

The common ratio in a geometric sequence can be found by dividing any term by the term that precedes it. For example, in the sequence 2, 6, 18, the common ratio is 6 / 2 = 3.

Tags

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 and d is the common difference.

Tags

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 and r is the common ratio.

Tags

CCSS.HSF.BF.A.2

Front

Identify whether the sequence 4, 8, 12, 16 is arithmetic, geometric, or neither.

Back

The sequence 4, 8, 12, 16 is an arithmetic sequence with a common difference of 4.

Tags

CCSS.HSF.BF.A.2

Front

Identify whether the sequence 2, 6, 18, 54 is arithmetic, geometric, or neither.

Back

The sequence 2, 6, 18, 54 is a geometric sequence with a common ratio of 3.

Tags

CCSS.HSF.BF.A.2

Front

What is the common difference of the arithmetic sequence 10, 15, 20, 25?

Back

The common difference is 5, as each term increases by 5.

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio of the geometric sequence 1, 3, 9, 27?

Back

The common ratio is 3, as each term is multiplied by 3.

Tags

CCSS.HSF.BF.A.2