Unit 5 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.

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.

Tags

CCSS.HSF.BF.A.2

Front

How do you determine if a sequence is arithmetic, geometric, or neither?

Back

To determine the type of sequence, check the differences between consecutive terms for arithmetic (constant difference) or the ratios for geometric (constant ratio). If neither condition is met, the sequence is neither.

Tags

CCSS.HSF.BF.A.2

Front

What is the formula for the n-th term of an arithmetic sequence?

Back

The n-th term of an arithmetic sequence can be expressed as 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 n-th term of a geometric sequence?

Back

The n-th term of a geometric sequence can be expressed as 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 a common difference in an arithmetic sequence?

Back

The common difference is the constant amount that each term in an arithmetic sequence increases or decreases by.

Tags

CCSS.HSF.BF.A.2

Front

What is a common ratio in a geometric sequence?

Back

The common ratio is the fixed number that each term in a geometric sequence is multiplied by to get the next term.

Tags

CCSS.HSF.BF.A.2

Front

Find the next three terms in the arithmetic sequence: 5, 10, 15, ...

Back

20, 25, 30

Tags

CCSS.HSF.BF.A.2

Front

Find the next three terms in the geometric sequence: 3, 6, 12, ...

Back

24, 48, 96

Tags

CCSS.HSF.BF.A.2

Front

What is the explicit formula for the arithmetic sequence: 2, 5, 8, ...?

Back

a_n = 2 + (n-1)3

Tags

CCSS.HSF.BF.A.2