Explicit and Recursive Rule

Front

What is an explicit rule in a sequence?

Back

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

Front

What is a recursive rule in a sequence?

Back

A recursive rule 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 7, 14, 28, 56, 112, what is the recursive formula?

Back

f(n) = f(n-1) * 2, f(1) = 7.

Front

What is the explicit formula for the sequence defined by a_n = 3(4)^n?

Back

The explicit formula is a_n = 3(4)^n, where n is the term number.

Front

How do you find the first four terms of the sequence a_n = 3(4)^n?

Back

Substitute n = 1, 2, 3, 4 into the formula: 12, 48, 192, 768.

Front

What is the explicit formula for the sequence defined by a_n = 7(n + 2)?

Back

The explicit formula is a_n = 7(n + 2), where n is the term number.

Front

How do you find the first four terms of the sequence a_n = 7(n + 2)?

Back

Substitute n = 1, 2, 3, 4 into the formula: 21, 28, 35, 42.

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 arithmetic sequence -3, -8, -13, -18, what are the next three terms?

Back

The next three terms are -23, -28, -33.

Front

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

Back

The common difference is -5.