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. This difference is called the common difference.

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.

Front

How do you determine if a sequence is arithmetic?

Back

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

Front

How do you determine if a sequence is geometric?

Back

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

Front

What is the common difference in the sequence: 5, 8, 11, 14, ...?

Back

The common difference is 3.

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

Find the common difference in the sequence: 10, 15, 20, 25, ...

Back

The common difference is 5.

Front

What is the 10th term in the arithmetic sequence: 3, 7, 11, 15, ...?

Back

The 10th term is 39.

Front

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

Back

The common ratio is 3.