Recursive and Explicit Formulas

Front

What is a recursive formula?

Back

A recursive formula defines the terms of a sequence using previous terms. For example, u_n = u_(n-1) - 3, where u_1 = 15.

Front

What is an explicit formula?

Back

An explicit formula provides a direct way to calculate the nth term of a sequence without referring to previous terms. For example, a_n = -2 + 5n.

Front

How do you find the first four terms of a sequence given an explicit formula?

Back

Substitute n = 1, 2, 3, and 4 into the explicit formula to find the corresponding terms.

Front

What is the first term of the sequence defined by u_n = u_(n-1) - 3 with u_1 = 15?

Back

The first term is 15.

Front

What is the common difference in the sequence 3, 8, 13, 18?

Back

The common difference is 5, as each term increases by 5.

Front

What does it mean for a sequence to be arithmetic?

Back

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

Front

Given the sequence 2, 7, 12, 17, what is the 5th term?

Back

The 5th term is 22.

Front

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

Back

The nth term can be expressed as a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is the significance of the first term in a recursive formula?

Back

The first term serves as the starting point for generating subsequent terms in the sequence.

Front

How do you determine if a sequence is defined recursively?

Back

A sequence is defined recursively if it specifies one or more initial terms and a rule for finding subsequent terms based on previous ones.