Sequences Table ChallengeComplete the tables showing the terms, formulas and sums of the arithmetic (linear) sequences. 
InstructionsTry your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help. When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file. 




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Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician? Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield: "I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information." Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay: "An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!" 
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Go MathsLearning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school. Maths MapAre you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.  
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❎Sequences  This is the basic sequences exercise that you should complete before starting this challenge.
Table 1  nth term of arithmetic sequences
Table 2  sum of n terms of arithmetic sequences
More levels are being considered to include other types of sequences.
Exam Style Questions  A collection of problems in the style of GCSE or IB/Alevel exam paper questions (worked solutions are available for Transum subscribers).
More Sequences Activities including lesson Starters, visual aids, investigations and selfmarking exercises.
Sequences Table Challenge was designed for those who have already completed the basic Sequences exercise (all levels). Here is the video that was made for that exercise.
Here is a reminder of some facts that may help you answering the questions in this exercise.
An arithmetic sequence, sometimes called an arithmetic progression, is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 8, 11, 14, 17, 20, 23, . . . is an arithmetic sequence with common difference of 3.
The first term of the sequence can be written as u_{1}
The n^{th} term of the sequence can be written as u_{n}
The common difference is usually written as d
The formula for finding the n^{th} term is u_{n}=u_{1}+(n1)d
The formula for finding the sum of n terms is S_{n}=½n(2u_{1}+(n1)d)
You can type in answers that are not whole numbers as decimals or mixed numbers (improper fractions not allowed). To type in a mixed number such as 4½ type in 4 space 1 / 2.
In the formula for the nth term don't mix decimals and fractions. For example \( \frac{1}{2}n+\frac{2}{5} \) and \(0.5n + 0.4 \) are both acceptable but \( \frac{1}{2}n+0.4 \) won't be recognised as correct by the program that checks answers.
Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can doubleclick the 'Check' button to make it float at the bottom of your screen.
Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.
These exercises use MathQuill, a web formula editor designed to make typing Maths easy and beautiful. Watch the animation below to see how common mathematical notation can be created using your keyboard.
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