In Exercises 1–14, write the first six terms of each arithmetic sequence. an = an-1 -0.4, a₁ = 1.6

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, each term is derived by adding or subtracting the common difference from the previous term.

Recursive Formula

A recursive formula defines each term of a sequence based on the preceding term(s). In this case, the formula an = an-1 - 0.4 indicates that each term is obtained by subtracting 0.4 from the previous term. Understanding how to apply recursive formulas is essential for generating terms in sequences.

Initial Term

The initial term, often denoted as a₁, is the first term of the sequence from which all subsequent terms are derived. In this problem, a₁ = 1.6 serves as the starting point for calculating the first six terms of the arithmetic sequence. Recognizing the initial term is crucial for accurately generating the sequence.