In Exercises 1–14, write the first six terms of each arithmetic sequence. a₁ = 200, d = 20

Verified step by step guidance

1. Identify the first term of the arithmetic sequence, which is given as a_1 = 200.
2. Recognize that the common difference (d) between consecutive terms is given as 20.
3. Use the formula for the n-th term of an arithmetic sequence: a_n = a_1 + (n-1) * d.
4. Calculate the second term: a_2 = a_1 + d = 200 + 20.
5. Continue calculating each subsequent term using the formula: a_3 = a_2 + d, a_4 = a_3 + d, a_5 = a_4 + d, a_6 = a_5 + d.

Key Concepts

Arithmetic Sequence

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the common difference (d). In this case, the first term (a₁) is 200, and the common difference is 20, meaning each term is obtained by adding 20 to the previous term.

First Term (a₁)

The first term of an arithmetic sequence, denoted as a₁, is the initial value from which the sequence begins. In this problem, a₁ is given as 200, which serves as the starting point for generating the subsequent terms of the sequence.

Common Difference (d)

The common difference (d) in an arithmetic sequence is the fixed amount added to each term to obtain the next term. In this example, d is 20, indicating that each term in the sequence will increase by 20 from the previous term, allowing for the calculation of the first six terms.