Textbook Question
In Exercises 11–16, a die is rolled. Find the probability of getting an odd number.
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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 11
Write the first six terms of each arithmetic sequence. an = an-1 -10, a1 = 30
Verified step by step guidance1
Identify the first term of the arithmetic sequence, which is given as \(a_1 = 30\).
Understand the recursive formula \(a_n = a_{n-1} - 10\), which means each term is 10 less than the previous term.
Calculate the second term by subtracting 10 from the first term: \(a_2 = a_1 - 10\).
Continue this process to find the third term: \(a_3 = a_2 - 10\).
Repeat the subtraction for the fourth, fifth, and sixth terms: \(a_4 = a_3 - 10\), \(a_5 = a_4 - 10\), and \(a_6 = a_5 - 10\).
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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 or subtracting a constant difference to the previous term. This constant difference is called the common difference. Understanding this helps in generating terms of the sequence.
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Recursive Formula for Sequences
A recursive formula defines each term of a sequence using the previous term(s). In this problem, the formula an = an-1 - 10 means each term is 10 less than the previous term. Recognizing how to use this formula is key to finding subsequent terms.
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Initial Term (a₁)
The initial term, denoted as a₁, is the first term of the sequence and serves as the starting point for generating all other terms. Knowing a₁ = 30 allows you to apply the recursive formula repeatedly to find the next terms.
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Related Practice
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Use the formula for nCr to evaluate each expression. 11C4
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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 a12 when a1 = 5, r = - 2
Textbook Question
Use mathematical induction to prove that each statement is true for every positive integer n. 4 + 8 + 12 + ... + 4n = 2n(n + 1)
Textbook Question
In Exercises 11–16, a die is rolled. Find the probability of getting a 4.
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Textbook Question
Use the Binomial Theorem to expand each binomial and express the result in simplified form.