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Find a formula for the general term $ a_n $ of the sequence, assuming that the pattern of the first few terms continues.$ \left\{\begin{array} 5, 8, 11, 14, 17, . . . . .\end{array}\right\} $

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Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 1

Sequences

Series

Campbell University

Harvey Mudd College

University of Nottingham

Boston College

Lectures

01:59

In mathematics, a series is, informally speaking, the sum of the terms of an infinite sequence. The sum of a finite sequence of real numbers is called a finite series. The sum of an infinite sequence of real numbers may or may not have a well-defined sum, and may or may not be equal to the limit of the sequence, if it exists. The study of the sums of infinite sequences is a major area in mathematics known as analysis.

02:28

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Formally, a sequence can be defined as a function whose domain is either the set of the natural numbers (for infinite sequences) or the set of the first "n" natural numbers (for a finite sequence). A sequence can be thought of as a list of elements with a particular order. Sequences are useful in a number of mathematical disciplines for studying functions, spaces, and other mathematical structures using the convergence properties of sequences. In particular, sequences are the basis for series, which are important in differential equations and analysis. Sequences are also of interest in their own right and can be studied as patterns or puzzles, such as in the study of prime numbers.

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Find a formula for the gen…

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The first several terms of…

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Find a formula for the nth…

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Find a general term $a_{n}…

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Find a formula for the $n$…

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Find a formula $a_{n}$ for…

So it looks like the terms are increasing by three every time. So are they in terms? They're gonna have some something here plus three end. Okay. And we know that our terms start at eight. So in order, Tio, make everything consistent. We should have a five there. You can check if you have vehicles one than you have five plus three, which is a and equals to you have five plus six, which is eleven. And then the next term will be fourteen because it'll just be three more Next time will be seventeen because it'll just be three more. That's what this three and is doing here.

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