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

Verified step by step guidance

1. Identify the first term of the arithmetic sequence, which is given as \(a_1 = 30\).
2. Understand the recursive formula \(a_n = a_{n-1} - 10\), which means each term is 10 less than the previous term.
3. Calculate the second term by subtracting 10 from the first term: \(a_2 = a_1 - 10\).
4. Continue this process to find the third term: \(a_3 = a_2 - 10\).
5. Repeat the subtraction for the fourth, fifth, and sixth terms: \(a_4 = a_3 - 10\), \(a_5 = a_4 - 10\), and \(a_6 = a_5 - 10\).

Key Concepts

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.