In Exercises 1–12, 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: $a{n}_{}={(}^{-}n(n+3)$.
2. Recall that the sequence terms are found by substituting positive integers for $n$, starting from 1.
3. Calculate the first term by substituting $n=\; 1$: $a\_1\; =\; (-1)^1\; (1\; +\; 3)$.
4. Calculate the second term by substituting $n=\; 2$: $a\_2\; =\; (-1)^2\; (2\; +\; 3)$.
5. Continue this process for $n=\; 3$ and $n=\; 4$ to find the third and fourth terms respectively.

Key Concepts

Sequences and General Terms

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

Exponentiation and Powers of -1

The expression (-1)^n alternates between -1 and 1 depending on whether n is odd or even. This causes the sequence terms to alternate in sign, which is important for determining the pattern of the sequence.

Substitution and Term Calculation

To find the first four terms, substitute n = 1, 2, 3, and 4 into the general term formula. Calculate each term step-by-step, paying attention to order of operations and sign changes.