Textbook Question
You are dealt one card from a standard 52-card deck. Find the probability of being dealt a queen.
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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 17
Find the indicated term of the arithmetic sequence with first term, , and common difference, d. Find a12 when a1 = -8, d = -2
Verified step by step guidance1
Identify the given values: the first term \(a_1 = -8\) and the common difference \(d = -2\).
Recall the formula for the \(n\)-th term of an arithmetic sequence: \(a_n = a_1 + (n - 1) \times d\).
Substitute \(n = 12\) into the formula to find the 12th term: \(a_{12} = a_1 + (12 - 1) \times d\).
Replace \(a_1\) and \(d\) with the given values: \(a_{12} = -8 + 11 \times (-2)\).
Simplify the expression step-by-step to find the value of \(a_{12}\).
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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, and the sequence progresses linearly.
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Common Difference (d)
The common difference is the fixed amount added to each term to get the next term in an arithmetic sequence. It can be positive, negative, or zero, and it determines the rate at which the sequence increases or decreases.
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Formula for the nth Term of an Arithmetic Sequence
The nth term (a_n) 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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Related Practice
Textbook Question
Find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a50 when a1 = 7, d = 5.
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Textbook Question
The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a1=4 and an=2an-1 + 3 for n≥2
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Textbook Question
Use the formula for nCr to evaluate each expression. 5C0
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The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a1=3 and an=4an-1 for n≥2
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Textbook Question
Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, a1 and common ratio, r. Find a8 when a1 = 1 000 000, r = 0.1
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