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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 51
Chapter 9, Problem 51

The general term of a sequence is given. Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. an = n + 5

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Identify the general term of the sequence: \(a_n = n + 5\).
Recall that an arithmetic sequence has a constant difference between consecutive terms, while a geometric sequence has a constant ratio between consecutive terms.
Calculate the first few terms of the sequence by substituting values of \(n\): for example, \(a_1 = 1 + 5\), \(a_2 = 2 + 5\), \(a_3 = 3 + 5\).
Find the differences between consecutive terms: \(a_2 - a_1\), \(a_3 - a_2\), and check if these differences are constant.
If the differences are constant, conclude the sequence is arithmetic and identify the common difference; if not, check the ratios \(\frac{a_2}{a_1}\), \(\frac{a_3}{a_2}\) to see if the sequence is geometric and find the common ratio if applicable.

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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 sequence of numbers where the difference between consecutive terms is constant. This constant difference is called the common difference. For example, in the sequence 2, 5, 8, 11, the common difference is 3.
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Geometric Sequence

A geometric sequence is a sequence where each term after the first is found by multiplying the previous term by a constant called the common ratio. For example, in the sequence 3, 6, 12, 24, the common ratio is 2.
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General Term of a Sequence

The general term (an) of a sequence is a formula that defines the nth term in terms of n. Understanding this formula helps identify the type of sequence and calculate specific terms, differences, or ratios as needed.
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Related Practice
Textbook Question

In Exercises 49–52, a single die is rolled twice. Find the probability of rolling an even number the first time and a number greater than 2 the second time.

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Use the Binomial Theorem to expand each expression and write the result in simplified form. (x1/3 +x-1/3)3

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Use the formula for nCr to solve Exercises 49–56. You volunteer to help drive children at a charity event to the zoo, but you can fit only 8 of the 17 children present in your van. How many different groups of 8 children can you drive?

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Use the graphs of the arithmetic sequences {a} and {b} to solve Exercises 51-58.

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Textbook Question

Use the formula for nCr to solve Exercises 49–56. Of 12 possible books, you plan to take 4 with you on vacation. How many different collections of 4 books can you take?