Textbook Question
Evaluate n!/(n-r)! for n = 20 and r = 3
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Ch. 8 - Sequences, Induction, and Probability
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 9, Problem 90
Exercises 88–90 will help you prepare for the material covered in the next section. Use the formula an = a₁3(n-1) to find the seventh term of the sequence 11, 33, 99, 297,...
Verified step by step guidance1
Identify the first term of the sequence, which is given as .
Recognize that the formula for the nth term of the sequence is , where 3 is the common ratio.
Substitute for in the formula to find the seventh term: .
Simplify the exponent by calculating , so the expression becomes .
To find the seventh term, multiply 11 by . (You can calculate first, then multiply by 11.)
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Geometric Sequence
A geometric sequence is a list of numbers where each term after the first is found by multiplying the previous term by a constant called the common ratio. In this problem, the sequence 11, 33, 99, 297,... is geometric with a common ratio of 3.
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Geometric Sequences - Recursive Formula
General Term Formula for Geometric Sequences
The nth term of a geometric sequence can be found using the formula an = a₁ * r^(n-1), where a₁ is the first term, r is the common ratio, and n is the term number. This formula allows direct calculation of any term without listing all previous terms.
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Exponentiation in Sequences
Exponentiation involves raising a number to a power, which in sequences represents repeated multiplication. In the formula an = a₁ * r^(n-1), the exponent (n-1) indicates how many times the common ratio is multiplied, crucial for finding terms like the seventh term.
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Related Practice
Textbook Question
A die is rolled. Find the probability of getting a number less than 3 or greater than 4.
Textbook Question
Evaluate n!/(n-r)!r! for n = 8 and r = 3
Textbook Question
How many four-digit odd numbers less than 6000 can be formed using the digits 2, 4, 6, 7, 8, and 9?
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Textbook Question
You are dealt one card from a 52-card deck. Find the probability of getting an ace or a king.
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Textbook Question
A die is rolled. Find the probability of getting a number less than 5.
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