Sequences

Front

What is a sequence?

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 has a constant difference between consecutive terms, while a geometric sequence has a constant ratio between consecutive terms.

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.

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The nth term can be calculated 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 common ratio in a geometric sequence?

Back

The common ratio is the fixed factor multiplied to each term to get the next term.

Front

What is the formula for the nth term of a geometric sequence?

Back

The nth term can be calculated using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

How do you determine if a sequence is geometric?

Back

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

Front

How do you determine if a sequence is arithmetic?

Back

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

Front

What is an example of an arithmetic sequence?

Back

An example of an arithmetic sequence is 2, 4, 6, 8, 10, where the common difference is 2.

Front

What is an example of a geometric sequence?

Back

An example of a geometric sequence is 3, 6, 12, 24, where the common ratio is 2.