27–34. Working with sequences Several terms of a sequence {aₙ}ₙ₌₁∞ are given.
a. Find the next two terms of the sequence.

{1, 3, 9, 27, 81, ......}

검증된 단계별 안내

Identify the pattern in the given sequence: {1, 3, 9, 27, 81, ......}. Notice how each term relates to the previous term.

Check if the sequence is geometric by dividing each term by the previous term. For example, calculate \( \frac{3}{1} \), \( \frac{9}{3} \), \( \frac{27}{9} \), and \( \frac{81}{27} \).

If the ratio between consecutive terms is constant, denote this common ratio as \( r \). This means the sequence is geometric and each term can be expressed as \( a_n = a_1 \times r^{n-1} \).

Use the common ratio \( r \) to find the next two terms by multiplying the last known term by \( r \) to get the next term, and then multiply that result by \( r \) again to get the term after that.

Write the expressions for the next two terms as \( a_6 = a_5 \times r \) and \( a_7 = a_6 \times r \), substituting the known values to express these terms explicitly.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

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주요 개념

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

Sequences and Terms

A sequence is an ordered list of numbers following a specific pattern. Each number in the sequence is called a term, typically denoted as aₙ, where n indicates the term's position. Understanding how terms relate helps predict future terms.

Geometric Sequences

A geometric sequence is one where each term is found by multiplying the previous term by a constant ratio. Identifying this ratio allows you to generate subsequent terms by repeated multiplication.

Pattern Recognition and Prediction

Recognizing the pattern in a sequence is essential to find missing or future terms. This involves analyzing the given terms, determining the rule (such as addition or multiplication), and applying it to extend the sequence.

27–34. Working with sequences Several terms of a sequence {aₙ}ₙ₌₁∞ are given.a. Find the next two terms of the sequence.{1, 3, 9, 27, 81, ......}