Use the formula a_n=4+(n-1)(-7) to find the eighth term of the sequence 4, −3, −10,…

Key Concepts

Arithmetic Sequence

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the common difference. In the given sequence, the first term is 4, and the common difference can be calculated as -7, indicating that each term is obtained by adding this constant to the previous term.

General Term Formula

The general term formula for an arithmetic sequence is expressed as a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, d is the common difference, and n is the term number. This formula allows us to find any term in the sequence without having to list all preceding terms, making it a powerful tool for analysis.

Substituting Values

Substituting values into the general term formula involves replacing the variables with specific numbers to calculate a particular term. For example, to find the eighth term (n=8) in the sequence, we substitute n into the formula a_n = 4 + (n-1)(-7) to compute the value of a_8, demonstrating the application of the formula in practice.