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 a_n to find a₂₀, the 20th term of the sequence. a₁ = 9, d=2

Verified step by step guidance

1. Recall that the general term (nth term) of an arithmetic sequence can be written as \(a_n = a_1 + (n - 1)d\), where \(a_1\) is the first term and \(d\) is the common difference.
2. Identify the given values: the first term \(a_1 = 9\) and the common difference \(d = 2\).
3. Substitute the given values into the general term formula to get \(a_n = 9 + (n - 1) \times 2\).
4. Simplify the expression to write the formula in a clearer form: \(a_n = 9 + 2n - 2\).
5. To find the 20th term, substitute \(n = 20\) into the formula: \(a_{20} = 9 + 2 \times 20 - 2\).

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 (d). For example, if the first term is 9 and the difference is 2, the sequence is 9, 11, 13, and so on.

General Term Formula of an Arithmetic Sequence

The general term (nth term) of an arithmetic sequence can be found using 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 allows direct calculation of any term without listing all previous terms.

Evaluating the nth Term

To find a specific term in the sequence, substitute the term number (n) into the general term formula. For example, to find the 20th term, plug n = 20 into the formula a_n = 9 + (20 - 1) * 2, then simplify to get the value of the 20th term.