In Exercises 12–15, write the first six terms of each arithmetic sequence. a1 = 3/2, d = -1/2

Verified step by step guidance

1. Identify the first term \(a_1\) of the arithmetic sequence, which is given as \(\frac{3}{2}\).
2. Recognize the common difference \(d\) of the sequence, which is \(-\frac{1}{2}\).
3. Use the formula for the \(n\)-th term of an arithmetic sequence: \(a_n = a_1 + (n-1) \cdot d\).
4. Calculate the second term \(a_2\) using the formula: \(a_2 = a_1 + d = \frac{3}{2} + (-\frac{1}{2})\).
5. Continue this process to find the next four terms \(a_3, a_4, a_5, a_6\) by repeatedly adding the common difference \(d\) to the previous term.

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 (d). In this case, the first term (a1) is given, and the common difference allows us to generate subsequent terms by adding d to the previous term.

First Term (a1)

The first term of an arithmetic sequence, denoted as a1, is the starting point of the sequence. It is essential for determining all other terms in the sequence. In this problem, a1 is given as 3/2, which serves as the foundation for calculating the following terms by repeatedly applying the common difference.

Common Difference (d)

The common difference (d) in an arithmetic sequence is the fixed amount that each term increases or decreases from the previous term. In this case, d is -1/2, indicating that each term will be 1/2 less than the term before it. This concept is crucial for generating the sequence's terms systematically.