Arithmetic/Geometric Sequences & Series

Front

What is the definition of 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 the definition of a geometric sequence?

Back

A geometric sequence is a sequence of numbers in which 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

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

Back

The n^th term of an arithmetic sequence can be calculated using the formula: a_n = a₁ + (n - 1)d, where a₁ 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 calculated using the formula: a_n = a₁ * r^(n-1), where a₁ is the first term and r is the common ratio.

Tags

CCSS.HSF.BF.A.2

Front

How do you determine if a sequence is arithmetic?

Back

A sequence is arithmetic if the difference between consecutive terms is constant.

Tags

CCSS.HSF.BF.A.2

Front

How do you determine if a sequence is geometric?

Back

A sequence is geometric if the ratio of consecutive terms is constant.

Tags

CCSS.HSF.BF.A.2

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the fixed amount added to each term to get the next term in an arithmetic sequence.

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio in a geometric sequence?

Back

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

Tags

CCSS.HSF.BF.A.2

Front

List the first five terms of the arithmetic sequence starting with 2 and having a common difference of 3.

Back

2, 5, 8, 11, 14.

Tags

CCSS.HSF.BF.A.2

Front

List the first five terms of the geometric sequence starting with 2 and having a common ratio of 3.

Back

2, 6, 18, 54, 162.

Tags

CCSS.HSF.BF.A.2