13–20. Explicit formulas Write the first four terms of the sequence { aₙ }∞ₙ₌₁.
aₙ = (−1)ⁿ / 2ⁿ

검증된 단계별 안내

Identify the general term of the sequence given by the formula \(a_n = \frac{(-1)^n}{2^n}\), where \(n\) is the term number starting from 1.

Calculate the first term \(a_1\) by substituting \(n=1\) into the formula: \(a_1 = \frac{(-1)^1}{2^1}\).

Calculate the second term \(a_2\) by substituting \(n=2\) into the formula: \(a_2 = \frac{(-1)^2}{2^2}\).

Calculate the third term \(a_3\) by substituting \(n=3\) into the formula: \(a_3 = \frac{(-1)^3}{2^3}\).

Calculate the fourth term \(a_4\) by substituting \(n=4\) into the formula: \(a_4 = \frac{(-1)^4}{2^4}\).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

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

Sequences and Terms

A sequence is an ordered list of numbers defined by a specific rule or formula. Each number in the sequence is called a term, denoted as aₙ, where n indicates the term's position. Understanding how to find terms from the explicit formula is essential for writing out the sequence.

Explicit Formula for Sequences

An explicit formula directly defines the nth term of a sequence as a function of n, allowing calculation of any term without knowing previous terms. For example, aₙ = (-1)ⁿ / 2ⁿ gives a direct way to compute each term by substituting n.

Exponentiation and Alternating Signs

Exponentiation involves raising a base to a power, such as 2ⁿ. The term (-1)ⁿ introduces alternating signs because (-1) raised to an even power is positive, and to an odd power is negative. This pattern affects the sign of each term in the sequence.

13–20. Explicit formulas Write the first four terms of the sequence { aₙ }∞ₙ₌₁. aₙ = (−1)ⁿ / 2ⁿ