Write the first six terms of each arithmetic sequence.
$a_1=-8,d=5$

Verified step by step guidance

1. Identify the first term of the arithmetic sequence, which is given as \(a_1 = -8\).
2. Recognize the common difference \(d = 5\), which means each term increases by 5 from the previous term.
3. Use the formula for the \(n\)-th term of an arithmetic sequence: \(a_n = a_1 + (n - 1) \times d\).
4. Calculate each of the first six terms by substituting \(n = 1, 2, 3, 4, 5, 6\) into the formula:
5. \(a_1 = -8\),
6. \(a_2 = -8 + (2 - 1) \times 5\),
7. \(a_3 = -8 + (3 - 1) \times 5\),
8. \(a_4 = -8 + (4 - 1) \times 5\),
9. \(a_5 = -8 + (5 - 1) \times 5\),
10. \(a_6 = -8 + (6 - 1) \times 5\).

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, and the sequence progresses linearly.

Common Difference (d)

The common difference is the fixed amount added to each term to get the next term in an arithmetic sequence. It can be positive, negative, or zero, and it determines the rate at which the sequence increases or decreases.

Finding Terms of an Arithmetic Sequence

To find any term in an arithmetic sequence, use the formula a_n = a_1 + (n - 1)d, where a_1 is the first term, d is the common difference, and n is the term number. This formula helps generate terms without listing all previous ones.