In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=(−3)^n

Key Concepts

Sequences

A sequence is an ordered list of numbers that follow a specific pattern or rule. Each number in the sequence is called a term, and the position of each term is typically denoted by an index, often starting from 1. Understanding sequences is fundamental in algebra as they can represent various mathematical phenomena and are used in functions, series, and more.

General Term of a Sequence

The general term of a sequence is a formula that allows you to calculate any term in the sequence based on its position. In this case, the general term is given by an = (-3)^n, where 'n' represents the term's position. This formula helps in generating the terms of the sequence without listing them all individually.

Exponential Functions

Exponential functions are mathematical functions of the form f(x) = a * b^x, where 'a' is a constant, 'b' is the base, and 'x' is the exponent. In the context of the sequence given, the term (-3)^n represents an exponential function with a base of -3. Understanding how exponential growth or decay works is crucial for analyzing the behavior of sequences defined by such terms.