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. For example, 2, 5, 8, 11 is an arithmetic sequence with a common difference of 3.

Tags

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.

Tags

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, d is the common difference, and n is the term number.

Tags

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

Tags

CCSS.HSF.BF.A.2

Front

What is the common difference in an arithmetic sequence?

Back

The common difference in an arithmetic sequence is the constant amount that each term increases or decreases by. For example, in the sequence 4, 7, 10, the common difference is 3.

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio in a geometric sequence?

Back

The common ratio in a geometric sequence is the factor by which each term is multiplied to get the next term. For example, in the sequence 2, 6, 18, the common ratio is 3.

Tags

CCSS.HSF.BF.A.2

Front

Identify if the sequence 5, 10, 15, 20 is arithmetic or geometric.

Back

The sequence 5, 10, 15, 20 is an arithmetic sequence because the difference between consecutive terms is constant (5).

Tags

CCSS.HSF.BF.A.2

Front

Identify if the sequence 2, 4, 8, 16 is arithmetic or geometric.

Back

The sequence 2, 4, 8, 16 is a geometric sequence because each term is multiplied by 2 to get the next term.

Tags

CCSS.HSF.BF.A.2

Front

What are the next three terms in the arithmetic sequence: 1, 4, 7, ...?

Back

The next three terms are 10, 13, 16.

Tags

CCSS.HSF.BF.A.2

Front

What are the next three terms in the geometric sequence: 3, 9, 27, ...?

Back

The next three terms are 81, 243, 729.

Tags

CCSS.HSF.BF.A.2