Write the first six terms of each arithmetic sequence. a_n = a_n-1 +6, a₁ = −9

Verified step by step guidance

1. Identify the given information: the first term \(a_1 = -9\) and the common difference \(d = 6\) (since \(a_n = a_{n-1} + 6\)).
2. Recall the formula for the \(n\)th term of an arithmetic sequence: \(a_n = a_1 + (n-1)d\).
3. Calculate the second term using the formula: \(a_2 = a_1 + (2-1) \times d = -9 + 1 \times 6\).
4. Find the third term similarly: \(a_3 = a_1 + (3-1) \times d = -9 + 2 \times 6\).
5. Continue this process to find the fourth, fifth, and sixth terms by substituting \(n=4, 5, 6\) into the formula \(a_n = -9 + (n-1) \times 6\).

Key Concepts

Arithmetic Sequence

An arithmetic sequence is a list of numbers where each term after the first is found by adding a constant difference to the previous term. This constant is called the common difference. For example, if the first term is -9 and the common difference is 6, the sequence progresses by adding 6 each time.

Recursive Formula for Sequences

A recursive formula defines each term of a sequence using the previous term. In this problem, the formula an = an-1 + 6 means each term is 6 more than the term before it. Understanding how to use this formula helps generate terms step-by-step.

Finding Terms of a Sequence

To find terms of a sequence given a recursive formula and the first term, start with the initial value and repeatedly apply the formula. For the first six terms, calculate each term by adding the common difference to the previous term, ensuring accuracy in each step.