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 an arithmetic sequence.

Front

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

Back

To find the next term, add the common difference to the last term.

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

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

Back

To find the next term, multiply the last term by the common ratio.

Front

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

Back

The nth term 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 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

If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 4th term?

Back

The 4th term is 5 + (4-1) * 3 = 14.

Front

If the first term of a geometric sequence is 2 and the common ratio is 3, what is the 3rd term?

Back

The 3rd term is 2 * 3^(3-1) = 18.