Arithmetic Sequences

An exercise on linear sequences including finding an expression for the nth term and the sum of n terms.

MatchsticksLevel 1Level 2Level 3Level 4Exam-StyleDescriptionHelpMore

This is level 4: mixed questions about linear sequences and their sums. You can earn a trophy if you get at least 7 questions correct and you do this activity online.

 What is the sum of the first ten terms of the sequence of even numbers? What is the sum of the first 50 terms of the sequence of odd numbers? The first four terms of an arithmetic sequence are 9, 17, 25, 33... Calculate the sum of the first 48 terms. The first four terms of an arithmetic sequence are 15, 21, 27, 33... Calculate the sum of the first 58 terms. The first four terms of an arithmetic sequence are 11, 24, 37, 50... Calculate the sum of the first 69 terms. Find the sum of this arithmetic series: -5 + 2 + 9 + 16 + ... + 226. Find the sum of this arithmetic series: -3 + 6.5 + 16 + 25.5 + ... + 177.5. There are eight houses in a row numbered 1 to 8. Phoebe lives in one of these houses and has noticed that the sum of the house numbers to her left is the same as the sum of the house numbers to her right. What is the number of Phoebe's house? There are 49 houses in a row numbered 1 to 49. Seren lives in one of these houses and has noticed that the sum of the house numbers to her left is the same as the sum of the house numbers to her right. What is the number of Seren's house? There are N houses in a row numbered 1 to N. Chris lives in the 204th house and has noticed that the sum of the house numbers to her left is the same as the sum of the house numbers to her right. Find the value of N.
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This is Arithmetic Sequences level 4. You can also try:
Matchsticks Level 1 Level 2 Level 3 Geometric Sequences

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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Sarah Murphy, Teacher

Monday, February 26, 2024

"For level 2 of this activity, it's not clear how the answer needs to be entered. In the help notes they make reference of things with subscripts. Guidance of the format to enter for the answer is needed.

[Transum: Thanks for your feedback Sarah. For level 2 the answer should be typed in as an expression (no equals sign) in its simplest form. For example, an answer might be '7n' or '5n-2'. No subscripts are required.]"

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Description of Levels

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Matchsticks - A beginner's exercise that lets you see how a sequence is structured.

Level 1 - Find the next term of these linear sequences

Level 2 - Find the nth term of these linear sequences

Level 3 - Find a given term of these linear sequences

Level 4 - Mixed questions about linear sequences and their sums

Missing Terms - Find the missing terms of arithmetic, geometric and Fibonacci-type sequences in this self marking quiz.

Exam Style questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.

Geometric Sequences - A similar exercise on geometric sequences.

Sigma - Practise using the sigma notation to find the sum of various number series.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Arithmetic Sequences

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)

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