General term
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The document provides examples of finding the general term of different sequences. For each sequence, it identifies the pattern between the terms and determines the formula for the nth term. The general terms provided are: 1) f(n) = 2n for the sequence 2, 4, 6, 8,... 2) f(n) = 2n - 1 for the sequence 1, 3, 5, 7,... 3) f(n) = 2n for the sequence 2, 4, 8, 16,... 4) f(n) = n^2 for the sequence 1, 4, 9, 16,... It also provides guidelines for finding the general term such as looking for a common difference,
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4
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Formula :𝑄𝑘 = LB +
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4
−𝑐𝑓𝑏
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𝑖
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N = total frequency
𝑐𝑓𝑏= cumulative frequency of the class before the 𝑄𝑘 class
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.
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𝑖 − 𝑐𝑙𝑎𝑠𝑠 𝑠𝑖𝑧𝑒
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4
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𝑖
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𝑄3−𝑄1
2
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(
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10)𝑁 − 𝑐𝑓
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𝑖 − 𝑐𝑙𝑎𝑠𝑠 𝑠𝑖𝑧𝑒
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The document provides information about sequences, including defining characteristics, types of sequences, general terms of sequences, recursive and explicit formulas, and examples. It discusses finite and infinite sequences, terms in a sequence, writing the general nth term as a function, and finding specific terms. Examples of sequences include the Fibonacci sequence and using the golden ratio in photography. Worked problems demonstrate finding terms of sequences given their formulas.
Arithmetic seqence
The document defines an arithmetic sequence as a sequence where a constant difference can be added between each term to get the next term. It provides examples of finding the first term and common difference of arithmetic sequences. It explains that the common difference is found by subtracting any term from the one that follows it. Formulas are provided for finding specific terms in an arithmetic sequence given the first term, common difference, or other information. Examples problems are worked through applying these concepts.
1103 ch 11 day 3
This document provides information about sequences and series. It defines sequences as functions with positive integers as the domain. It distinguishes between infinite and finite sequences. Examples of sequences are provided and explicit formulas for finding terms are derived. Methods for finding the nth term of arithmetic and geometric sequences are described.
9.4 part 1.ppt worked
This document provides information and examples about number patterns, sequence notation, recursive and explicit definitions of sequences, arithmetic sequences, and formulas for finding terms in arithmetic sequences. It includes examples of identifying arithmetic sequences, finding common differences, using recursive and explicit formulas to find specific terms, and using the arithmetic mean to find missing terms. Students are assigned a worksheet to complete problems related to these concepts but are asked to wait on questions 16-20 until they can be discussed.
Sequence
A sequence is a set of numbers written in a given order. It is a function whose domain is the set of natural numbers and whose range is a subset of real numbers. Terms are the numbers or values in the sequence. A finite sequence has a last term, while an infinite sequence continues without end. Examples show finite sequences have a defined last term, while infinite sequences use ellipses to indicate they continue indefinitely. Finding a sequence's term or general pattern allows determining future terms from the given terms.
Harmonic sequence
The document discusses harmonic sequences. A harmonic sequence is a sequence whose reciprocals form an arithmetic sequence. It provides examples of determining terms of harmonic sequences. It explains that the terms between any two terms of a harmonic sequence are called harmonic means. An example is worked out of inserting two harmonic means between two given terms of a harmonic sequence.
Grade 10 Math Module 1 searching for patterns, sequence and series
This module introduces sequences and their different types. It discusses finding patterns in sequences to determine the next term. Specific examples are provided to demonstrate writing the first few terms of a sequence given its general formula. The key concepts covered are defining sequences, finite vs infinite sequences, terms of a sequence, increasing vs decreasing sequences, and using the general formula to find specific terms. Students are expected to be able to list terms of sequences, derive the formula, generate terms recursively, and describe arithmetic sequences in different ways.
Chapter 1 sequences and series
The document discusses sequences and series, including arithmetic and geometric sequences and series. It provides examples and formulas to find terms of sequences and the sums of finite and infinite series. It also gives exercises with solutions to apply these concepts, such as finding specific terms, determining sums, and solving application problems involving sequences and series.
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This document discusses geometric sequences and series. It defines a geometric sequence as a sequence whose consecutive terms have a common ratio. The nth term of a geometric sequence can be found using the formula an = a1rn-1, where a1 is the first term and r is the common ratio. It also provides the formula to find the sum of a finite geometric series, which is S = a1(1-rn)/(1-r), where S is the sum, a1 is the first term, r is the common ratio, and n is the number of terms. Several examples are provided to demonstrate finding terms, sums, and determining if a sequence is geometric.
Presentation4
This document discusses sequences and their properties. It defines sequences and provides examples of different types of sequences including arithmetic, geometric, harmonic, and Fibonacci sequences. It discusses finding formulas for the nth term of sequences and calculating sums of sequence terms. Examples are provided to demonstrate finding sequence terms, recognizing sequence types based on patterns of terms, and using recurrence relations to define sequences.
Arithmetic Sequences
An arithmetic sequence is a sequence where the difference between consecutive terms is constant. The common difference (d) is this constant value. The recursive formula for an arithmetic sequence is Un = Un-1 + d and the explicit formula is Un = U1 + (n - 1)d. Given values for the first few terms, you can find the common difference and write the recursive and explicit formulas to generate all terms of the sequence.
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This document provides an introduction to sequences and series. It begins with definitions of sequences, series, arithmetic progressions, geometric progressions and their key terms. It then presents several examples of finding terms in arithmetic and geometric progressions. The document also defines arithmetic mean and geometric mean, and discusses how to find the sum of terms in an arithmetic progression using formulas. Overall, the document serves as an introductory guide to common concepts involving sequences and progressions.
(678215997) neethutext
This document provides an introduction to sequences and series. It begins with definitions of sequences, finite and infinite sequences, and series. It then covers topics like arithmetic progressions, geometric progressions, and harmonic progressions. It provides formulas for the nth term and sum of terms for arithmetic and geometric progressions. It also defines arithmetic mean and geometric mean between terms in progressions. The document aims to help secondary students understand key concepts related to sequences and series.
Successful Minds,Making Mathematics number patterns &sequences Simple.
This document provides information about number patterns and sequences. It discusses arithmetic sequences where the difference between consecutive terms is constant, and quadratic patterns where the second differences are constant. Examples are provided to demonstrate how to determine the general term of a sequence from a given pattern. Practice problems with solutions allow the reader to apply the concepts to find missing terms, general terms, and values of specific terms.
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General term
- 1. Finding General Term of a Sequence
- 2. Example 1. Find the general term of the sequence 2, 4, 6, 8, … Solution Observe the following. 2 = 2(1) – means 1st term 4 = 2(2) - 2nd term 6 = 2(3) - 3rd term 8 = 2(4) - 4th term ⋮ ⋮ The pattern is 2n where n = 1, 2, 3, 4, … or n is the position of each term in a sequence. So, the general term of the sequence is f(n) = 2n.
- 3. Example 2. Find the general term of the sequence 1, 3, 5, 7, … Solution Observe the following. 1 = 2(1) – 1 3 = 2(2) – 1 5 = 2(3) – 1 7 = 2(4) – 1 ⋮ ⋮ The pattern is 2n – 1 where n = {1, 2, 3, 4, …}. So, the general term of the sequence is f(n) = 2n – 1.
- 4. Example 3. Find the general term of the sequence 2, 4, 8, 16, … Solution We can express in this manner: 2 = 21 4 = 22 8 = 23 16 = 24 ⋮ ⋮ The pattern is is 2n where n = {1, 2, 3, 4, …}. So, the general term of the sequence is f(n) = 2n.
- 5. Example 4. Find the general term of the sequence 1, 4, 9, 16, … Solution We can be express each term in the following manner: 1 = (1)2 4 = (2)2 9 = (3)2 16 = (4)2 ⋮ ⋮ The pattern is n2 where n = {1, 2, 3, 4, …}. So, the general term of the sequence is f(n) = n2 .
- 6. Theres no definite way or rule in finding the nth term of a given sequences. The following are helpful guide. • 1. Find out if there is a common difference between two terms of the given sequence of numbers. • 2. Find out if there is a common factor among the terms of the given sequences of numbers. • 3. Find out if the given sequence is expressible in exponential form with a common base.