Recursive and Explicit formulas

Front

What is a recursive formula?

Back

A recursive formula defines the terms of a sequence using previous terms. It specifies how to calculate the next term based on one or more preceding terms.

Front

What is an explicit formula?

Back

An explicit formula provides a direct way to calculate the nth term of a sequence without needing to know the previous terms.

Front

Given the recursive formula a_n = a_{n-1} + d, what does 'd' represent?

Back

In this formula, 'd' represents the common difference between consecutive terms in an arithmetic sequence.

Front

How do you find the first four terms of a sequence defined by a recursive formula?

Back

To find the first four terms, start with the initial term and repeatedly apply the recursive formula to generate subsequent terms.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the constant amount that each term increases or decreases by from the previous term.

Front

How can you identify the common difference from a sequence?

Back

Subtract any term from the term that follows it. The result will be the common difference.

Front

Write the explicit formula for the arithmetic sequence defined by the first term a_1 and common difference d.

Back

The explicit formula is a_n = a_1 + (n-1)d.

Front

What is the 10th term of the sequence defined by a_n = a_1 + (n-1)d?

Back

To find the 10th term, substitute n=10 into the explicit formula: a_{10} = a_1 + 9d.

Front

How do you derive an explicit formula from a given sequence?

Back

Identify the first term and the common difference, then use the formula a_n = a_1 + (n-1)d.

Front

What is the first term of the sequence defined by a_1 = 9 and a_n = a_{n-1} + 8?

Back

The first term a_1 is 9.