In Exercises 23–34, 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 to find the 20th term of the sequence. a1=-20, d = -4

Verified step by step guidance

1. Identify the first term \( a_1 = -20 \) and the common difference \( d = -4 \) of the arithmetic sequence.
2. Recall the formula for the general term \( a_n \) of an arithmetic sequence: \( a_n = a_1 + (n-1) \cdot d \).
3. Substitute the given values into the formula: \( a_n = -20 + (n-1) \cdot (-4) \).
4. Simplify the expression to find the general term formula: \( a_n = -20 - 4(n-1) \).
5. To find the 20th term, substitute \( n = 20 \) into the general term formula and simplify.

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 the given problem, the first term (a1) is -20, and the common difference is -4, indicating that each term is obtained by subtracting 4 from the previous term.

General Term Formula

The general term (nth term) of an arithmetic sequence can be expressed using the formula: a_n = a1 + (n - 1)d, where a_n is the nth term, a1 is the first term, d is the common difference, and n is the term number. 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, substitute the desired term number (n) into the general term formula. For example, to find the 20th term, you would set n = 20 in the formula a_n = a1 + (n - 1)d, which allows you to compute the value of that term directly based on the first term and the common difference.