In Exercises 19–21, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for an to find a20, the 20th term of the sequence. -7, -3, 1, 5 ...

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, denoted as 'd'. For example, in the sequence -7, -3, 1, 5, the common difference is 4, as each term increases by 4 from the previous term.

General Term Formula

The general term formula for an arithmetic sequence can be expressed as a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference. This formula allows us to calculate any term in the sequence without needing to list all previous terms.

Finding Specific Terms

To find a specific term in an arithmetic sequence, such as a_20, we substitute n with 20 in the general term formula. By calculating a_20 = a_1 + (20 - 1)d, we can determine the value of the 20th term directly, using the first term and the common difference established in the sequence.