Intro to Sequences CW

Front

What is a sequence in mathematics?

Back

A sequence is an ordered list of numbers that follow a specific pattern or rule.

Front

What is the difference between an arithmetic sequence and a geometric sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant, while a geometric sequence is a sequence where each term is found by multiplying the previous term by a fixed, non-zero number.

Front

How do you find the next term in an arithmetic sequence?

Back

To find the next term in an arithmetic sequence, add the common difference to the last term.

Front

How do you find the next term in a geometric sequence?

Back

To find the next term in a geometric sequence, multiply the last term by the common ratio.

Front

What is the common difference in the sequence 10, 20, 30, 40?

Back

The common difference is 10.

Front

What is the common ratio in the sequence 2, 6, 18, 54?

Back

The common ratio is 3.

Front

How do you identify the pattern in a sequence?

Back

To identify the pattern in a sequence, look for a consistent operation (addition, subtraction, multiplication, or division) applied to the terms.

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.

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.

Front

What is a missing term in a sequence?

Back

A missing term in a sequence is a term that is not provided but can be calculated based on the established pattern of the sequence.