Sequences: Explicit & Recursive Formulas

Front

What is a sequence?

Back

A sequence is a set of numbers in a specific order.

Front

What is an explicit formula for a sequence?

Back

An explicit formula defines the nth term of a sequence directly in terms of n.

Front

What is a recursive formula for a sequence?

Back

A recursive formula defines each term of a sequence using the previous term(s).

Front

Find the first four terms of the sequence defined by a_n = 6n - 1.

Back

5, 11, 17, 23.

Front

Which sequence has a pattern of 'multiply by 4'?

Back

3, 12, 48, 192.

Front

What is the common difference in the sequence 2, 7, 12, 17,...?

Back

The common difference is 5.

Front

Given a_n = 7, what is a_n+1 in the sequence 2, 7, 12, 17,...?

Back

12.

Front

What is the first term of the sequence defined by a_n = 3n + 2?

Back

5.

Front

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

Back

Use the formula a_n = a_1 + (n-1)d, where d is the common difference.

Front

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

Back

a_n = a_1 * r^(n-1), where r is the common ratio.