Write the first four terms of each sequence whose general term is given. a_n=(−1)ⁿ(n+3)

Verified step by step guidance

1. Identify the general term of the sequence given by the formula \(a_n = (-1)^{n}(n+3)\), where \(n\) represents the term number.
2. To find the first four terms, substitute \(n = 1, 2, 3,\) and \$4$ into the formula one at a time.
3. Calculate \(a_1\) by substituting \(n=1\): \(a_1 = (-1)^{1}(1+3)\).
4. Calculate \(a_2\) by substituting \(n=2\): \(a_2 = (-1)^{2}(2+3)\).
5. Similarly, calculate \(a_3\) and \(a_4\) by substituting \(n=3\) and \(n=4\) into the formula: \(a_3 = (-1)^{3}(3+3)\) and \(a_4 = (-1)^{4}(4+3)\).

Key Concepts

Sequences and General Terms

A sequence is an ordered list of numbers defined by a general term formula a_n, which gives the nth term. Understanding how to use the general term allows you to find specific terms by substituting values of n.

Evaluating Expressions with Exponents

The term (−1)^n alternates the sign of each term depending on whether n is even or odd. Recognizing this pattern helps determine if a term is positive or negative, which is essential for correctly calculating sequence terms.

Substitution and Simplification

To find the first four terms, substitute n = 1, 2, 3, and 4 into the general term and simplify each expression. This process involves arithmetic operations and careful handling of signs to accurately compute each term.