Explicit and Recursive Formulas

Front

What is an explicit formula?

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?

Back

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

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

Given the sequence 2, 5, 8, 11, 14, what is the common difference?

Back

The common difference is 3, as each term increases by 3.

Front

Write the recursive formula for the sequence 2, 5, 8, 11, 14.

Back

a_1 = 2; a_n = a_{n-1} + 3.

Front

Write the explicit formula for the sequence 2, 5, 8, 11, 14.

Back

a_n = 3n - 1.

Front

What is the first term of the sequence defined by a_n = a_{n-1} + 4 if a_1 = 1?

Back

The first term is 1.

Front

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

Back

a_n = a_{n-1} - 16.

Front

Identify the arithmetic sequence: 1, 3, 5, 7, 9 or 1, 2, 4, 8, 16?

Back

1, 3, 5, 7, 9 is the arithmetic sequence.

Front

What is the explicit formula for the sequence 1, 3, 5, 7, 9?

Back

a_n = 2n - 1.