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Sequences Table Challenge

Complete the tables showing the terms, formulas and sums of the arithmetic (linear) sequences.

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\(u_1\) \(u_2\) \(u_3\) \(u_4\) \(d\) \(u_n\) \(u_{8}\) \(u_{76}\)

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Instructions

Try 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.

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Description of Levels

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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/A-level exam paper questions (worked solutions are available for Transum subscribers).

More Sequences Activities including lesson Starters, visual aids, investigations and self-marking exercises.

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.

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Help Video For The Basic Sequences Exercise

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 u1

The nth term of the sequence can be written as un

The common difference is usually written as d

The formula for finding the nth term is un=u1+(n-1)d

The formula for finding the sum of n terms is Sn=½n(2u1+(n-1)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 double-click 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.

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Typing Mathematical Notation

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.

MathQuill Animation

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