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

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Identify the general term of the sequence given by the formula \(a_n = (-1)^{n}(n+3)\), where \(n\) represents the term number.

To find the first four terms, substitute \(n = 1, 2, 3,\) and \(4\) into the formula one at a time.

Calculate \(a_1\) by substituting \(n=1\): \(a_1 = (-1)^{1}(1+3)\).

Calculate \(a_2\) by substituting \(n=2\): \(a_2 = (-1)^{2}(2+3)\).

Similarly, calculate \(a_3\) and \(a_4\) by substituting \(n=3\) and \(n=4\) into the formula: \(a_3 = (-1)^{3}(3+3)\) and \(a_4 = (-1)^{4}(4+3)\).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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