Sequences and Series notes
21 notes by 19 users
This Sequences and Series page on GoConqr gathers user-made notes on number patterns, nth-term rules and convergence. It is for school students, university students and professional candidates practising sequences and series, as well as teachers looking for ready-made material. There are more than 10 notes, spanning school and university study. Choose a note to explore.
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- Number Patterns17
- Nth Term of a Sequence29
- Arithmetic and Geometric Sequences and Series32
- Arithmetic Sequences and Series42
- Geometric Sequences and Series13
- Recurrence Relations and the Fibonacci Sequence10
- Sigma Notation and Series Sums6
- Limits and Convergence of Sequences5
- Series Convergence Tests8
- Power Series and Taylor Series8
Notes
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Nth Term- By Rafail Zintro What are the nth term and the 10th term of this sequence: 2, 4, 6, ... ?nth term = 2n10th term = 20. To work this out, n = 10, so 2n = 2 × 10 = 20 What is the nth term of this sequence? 1st = ...
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Series and Sequences Sequences (Nth term) Sequences are sets of ranges which follow the pattern U1, U2, U3, U4 .... Un 3 , 7, 11, 15 ... Un +4 +4 +4 is the common difference So we can say 4n is the basis of ...
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The nth Term The nth termYou can find a term in a sequence using a position-to-term rule, if you know the terms position.Example Position in sequence 1 2 &nb...
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Number Sequences Number Sequences August 18th 2014 Book 1, Chapter 6
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Chapter 9 notes
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Math revision guide Finding HCFs and LCMs of larger numbers Example Find the LCM 60 and 504 Find the largest power of each prime factor that appears in either number Multiply these powers of primes together&n...
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Sequences Sequences A set of numbers arranged in a particular order# The simplest sequence: sequence of natural numbers e.g - (counting numbers) 1,2,3,4,5,6,7,8,9,10,11.....................
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9.1: Sequences - created from Mind Map Chapter 9: Infinite Series Checklist of Key Ideas: Purpose: How to determine if they converge
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Series and Sequences An arithmetic series (or progression) is a series where each term is obtained by adding on a constant to the previous term. The series goes up in equal steps.The constant is called the common difference (d).An arithme...
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Nth term rule a) From looking at the sequence we can see that each term is 6 larger than the previous term. We say the term-to-term rule is "add 6". Therefore the next two terms are 34 and 40.b) The nth term of a sequence is a...
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quadratic sequences okay so today in this resource, I am going to tell you how to work out a quadratic sequence if anyone needs help, feel free to ask Example 1, 4, 9, 16, 25, 36 okay so first you have to work out the difference of...
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MATHEMATICS 07.20.2020 SEQUENCE AND SERIES READ MODULE AND ANSWER PAGE 18 SEQUENCE mathematically, a sequence is just a succession of numbers in a specific order. » each number in a sequence is called a term. ...
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Untitled Q Working out the Nth term of a sequencenth term 1 2 3 4 5Original number 1 5 9 13 17Difference between each term 4 4 4 4 Working out the Nth term of a sequence
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Arithmetic_Mixed_Problems (Practice Exercises) Formula: Arithmetic Sequence The nth term of an arithmetic sequence: Un = U1 + (n - 1) d The sum of n terms of an arithmetic sequence: Sn = n/2 (2 U1 + (n - 1) d) Sn = n/2 (U...
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Number sequences WHAT EVEN IS A NUMBER SQUENCE? A sequence, in mathematics, is a string of objects, like numbers, that follow a particular pattern. The individual elements in a sequence are called terms. Some of the simplest sequences...
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1_Number sequences WHAT EVEN IS A NUMBER SQUENCE? A sequence, in mathematics, is a string of objects, like numbers, that follow a particular pattern. The individual elements in a sequence are called terms. Some of the simplest sequences...
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Series
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Hegarty maths Attempt 1 Hegarty 1.What is the nth term rule of the linear sequence below?7,9,11,13,15 = 2n+5 2.What is the nth term rule of the linear sequence below?−4,−1,2,5,8,= 3n-1 x 3n-7 3.What is the nth term rule...
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number pattern 2 Rectangular NumbersRectangular numbers are all natural numbers except 1 and prime numbers. Examples are 6, 8,15, 2 etc. Note that 2 is a peculiar number. Though it is an even number, it is a rectangular number. Triang...
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Maths Assignment 1. Write down the next three terms of the sequence.I) 1,2,4,8,16,...ii) 2,5,8,11,14,...iii) 1,4,9,16,...2. Explain the followingI) Rectangular numbersii) Square numbersiii) Triangular numbersiv) Perfect Square3. find ...
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Untitled Write an expression in terms of n for the sequence: 4,7,12,19,28 1st difference: 3,5,7,9 2nd...
More Sequences and Series resources
About sequences and series notes
GoConqr OriginalSequences and Series notes
These notes offer different ways into the unit. The nth Term uses a table to show a position-to-term rule. Series and Sequences includes notes on arithmetic series and common differences. Other notes look at quadratic sequences, while Chapter 9 notes describes defining a sequence explicitly.
How to use the notes
Start with The nth Term if you want an example of linking each position to a term. Read the table, then cover the rule and see whether you can recover it from the terms. The notes on quadratic sequences offer another pattern to examine when you are ready.
For a broader look at infinite sequences, read the notes on finding a formula for the nth term and determining convergence. If you want to check your understanding after reading, switch to a quiz on the unit page. You can also use a mind map there to review connections between ideas.
Pick a note that matches the part of the unit you are studying.
Frequently asked questions
Which note is a useful starting point for nth-term rules?
The nth Term is a useful place to start. It shows positions and corresponding terms in a table, then gives a rule for the nth term. You can follow that with Nth term rule, which distinguishes a term-to-term rule from an nth-term rule.
Do the notes cover more than simple number patterns?
Yes. Alongside notes on number patterns and nth-term rules, the page lists notes on quadratic sequences, arithmetic series and convergence. Chapter 9 notes also describes defining a sequence explicitly, so there are different topics to choose from as you work through the unit.
Are these notes free to use?
Yes. Every note listed here is free to open and study without an account. The resources were made by GoConqr users. A free account additionally lets you save quiz scores and make your own quizzes, mind maps, flashcards and notes.