Textbook Question
In Exercises 12–15, write the first six terms of each arithmetic sequence. a1 = 3/2, d = -1/2
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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 15
Find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a6 when a1 = 13, d = 4.
Verified step by step guidance1
Identify the given information: the first term \(a_1 = 13\) and the common difference \(d = 4\).
Recall the formula for the \(n\)-th term of an arithmetic sequence: \(a_n = a_1 + (n - 1) \times d\).
Substitute \(n = 6\) into the formula to find the 6th term: \(a_6 = 13 + (6 - 1) \times 4\).
Simplify the expression inside the parentheses: \(6 - 1 = 5\), so the formula becomes \(a_6 = 13 + 5 \times 4\).
Multiply and add to express \(a_6\) in terms of known values: \(a_6 = 13 + 20\) (do not calculate the final sum).
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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, denoted by d. Understanding this helps identify the pattern and predict any term in the sequence.
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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. Knowing d allows you to calculate any term in the sequence using the formula for the nth term.
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Formula for the nth Term of an Arithmetic Sequence
The nth term (a_n) of an arithmetic sequence is given by 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 is essential for finding specific terms like a_6 in the sequence.
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Related Practice
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In Exercises 11–16, a die is rolled. Find the probability of getting a number greater than 4.
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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