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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 29
Chapter 9, Problem 29

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=-20, d = -4

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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 \(a_1 = -20\) and the common difference \(d = -4\).
Substitute these values into the general term formula to get \(a_n = -20 + (n - 1)(-4)\).
Simplify the expression inside the parentheses: \(a_n = -20 - 4(n - 1)\).
To find the 20th term, substitute \(n = 20\) into the formula: \(a_{20} = -20 - 4(20 - 1)\).

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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). Understanding this pattern is essential to write formulas and find specific terms.
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General Term Formula of an Arithmetic Sequence

The general term (nth term) of an arithmetic sequence is given by the formula an = a1 + (n - 1)d, where a1 is the first term, d is the common difference, and n is the term number. This formula allows direct calculation of any term without recursion.
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Evaluating the nth Term

Once the general term formula is established, substituting the desired term number (like n=20) into the formula yields the specific term's value. This step involves simple arithmetic and is crucial for solving problems that ask for a particular term.
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