3.4 Explicit & Recursive Formula

Front

What is an explicit formula in a sequence?

Back

An explicit formula defines the nth term of a sequence directly in terms of n, allowing you to calculate any term without needing to know the previous terms.

Front

What is a recursive formula in a sequence?

Back

A recursive formula defines each term of a sequence based on the previous term(s), requiring knowledge of earlier terms to find the next term.

Front

Given the sequence 2, 8, 14, ..., what is the explicit formula?

Back

a_n = 6n - 4.

Front

What is the value of a_3 in the sequence 4, 11, 18, 25...?

Back

a_3 = 18.

Front

How do you find the explicit equation for the sequence 25, 21, 17, 13...?

Back

The explicit equation is a_n = -4n + 29.

Front

What is the recursive rule for the sequence 17, 1, -15, -31...?

Back

a_n = a_{n-1} - 16.

Front

What are the next two terms of the sequence 4, 7, 10, 13?

Back

The next two terms are 16 and 19.

Front

How do you derive an explicit formula from a sequence?

Back

Identify the pattern in the sequence, determine the common difference or ratio, and express the nth term in terms of n.

Front

What is the common difference in the sequence 4, 11, 18, 25...?

Back

The common difference is 7.

Front

What does the term 'sequence' mean in mathematics?

Back

A sequence is an ordered list of numbers that follow a specific pattern or rule.