Domanda del libro di testo
Use the graphs of the arithmetic sequences {a} and {b} to solve Exercises 51-58. If {an} is a finite sequence whose last term is -83, how many terms does {an} contain?
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Ch. 8 - Sequences, Induction, and Probability
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- 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
Capitolo 9, Problema 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
Guida verificata passo dopo passo1
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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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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Arithmetic Sequences - General Formula
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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4:18Geometric Sequences - Recursive Formula
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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4:45Geometric Sequences - General Formula
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