Write the first six terms of each arithmetic sequence. a_n = a_n-1 -10, a₁ = 30

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Identify the first term of the arithmetic sequence, which is given as \(a_1 = 30\).

Understand the recursive formula \(a_n = a_{n-1} - 10\), which means each term is 10 less than the previous term.

Calculate the second term by subtracting 10 from the first term: \(a_2 = a_1 - 10\).

Continue this process to find the third term: \(a_3 = a_2 - 10\).

Repeat the subtraction for the fourth, fifth, and sixth terms: \(a_4 = a_3 - 10\), \(a_5 = a_4 - 10\), and \(a_6 = a_5 - 10\).

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주요 개념

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

Arithmetic Sequence

An arithmetic sequence is a list of numbers where each term after the first is found by adding or subtracting a constant difference to the previous term. This constant difference is called the common difference. Understanding this helps in generating terms of the sequence.

Recursive Formula for Sequences

A recursive formula defines each term of a sequence using the previous term(s). In this problem, the formula an = an-1 - 10 means each term is 10 less than the previous term. Recognizing how to use this formula is key to finding subsequent terms.

Initial Term (a₁)

The initial term, denoted as a₁, is the first term of the sequence and serves as the starting point for generating all other terms. Knowing a₁ = 30 allows you to apply the recursive formula repeatedly to find the next terms.

Write the first six terms of each arithmetic sequence. an = an-1 -10, a1 = 30