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Ch. 8 - Sequences, Induction, and Probability
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 8 - Sequences, Induction, and ProbabilityProblem 27
Chapter 9, Problem 27

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. a1 = 9, d=2

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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.
Identify the given values: the first term \(a_1 = 9\) and the common difference \(d = 2\).
Substitute the given values into the general term formula to get \(a_n = 9 + (n - 1) \times 2\).
Simplify the expression to write the formula in a clearer form: \(a_n = 9 + 2n - 2\).
To find the 20th term, substitute \(n = 20\) into the formula: \(a_{20} = 9 + 2 \times 20 - 2\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.
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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.
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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.
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