Introduction to 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 an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

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 the sequence.

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

What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which we multiply each term to get the next term in the sequence.

Front

How do you find the nth term of an arithmetic sequence?

Back

The nth term can be found using the formula: a_n = a_1 + d(n - 1), where a_1 is the first term, d is the common difference, and n is the term number.

Front

How do you find the nth term of a geometric sequence?

Back

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

Front

What is the first term of the sequence 2, 8, 32, 128?

Back

The first term is 2.

Front

What is the common difference of the arithmetic sequence -6, -1, 4, 9?

Back

The common difference is 5.

Front

What is the next term in the sequence 11, 8, 5, 2?

Back

The next term is -1.