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Geometric SequencesAn exercise on geometric sequences including finding the nth term and the sum of n terms. |
This is level 1: find the next term of these geometric sequences. You will be awarded a trophy if you get at least 9 answers correct and you do this activity online.
This is Geometric Sequences level 1. You can also try:
Arithmetic Sequences
Level 2
Level 3
Level 4
Level 5
Quadratic 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 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College: "Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work" Comment recorded on the 9 May 'Starter of the Day' page by Liz, Kuwait: "I would like to thank you for the excellent resources which I used every day. My students would often turn up early to tackle the starter of the day as there were stamps for the first 5 finishers. We also had a lot of fun with the fun maths. All in all your resources provoked discussion and the students had a lot of fun." |
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Featured ActivityRoman Numerals Jigsaw This is a wonderful activity for someone who does not know Roman numerals. By completing the activity an understanding of the symbols develops and a great sense of achievement is enjoyed. |
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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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❎Level 1 - Find the next term of these geometric sequences
Level 2 - Find a given term of these geometric sequences
Level 3 - Find the first five terms of the sequence given the formula
Level 4 - Mixed questions about geometric sequences and their sums
Level 5 - Sum of infinite convergent geometric sequences
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.
Arithmetic Sequences - A similar exercise on arithmetic sequences.
Sigma - Practise using the sigma notation to find the sum of various number series.
More on this topic including lesson Starters, visual aids and investigations.
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.
See the National Curriculum page for links to related online activities and resources.
Here is a reminder of some facts that may help you answering the questions in this exercise.
An geometric sequence, sometimes called a geometric progression, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed number called the common ratio. For example, the sequence 5, 10, 20, 40, ... is a geometric sequence with common ratio 2.
The first term of the sequence can be written as u1
The nth term of the sequence can be written as un
The common ratio is usually written as r
The formula for finding the nth term is un=u1r(n-1)
The formula for finding the sum of \(n\) terms is:
$$ S_n = \dfrac{u_1(r^n-1)}{r-1}$$The sum of an infinite geometric sequence is:
$$ S_\infty = \dfrac{u_1}{1-r}, \quad |r| \lt 1 $$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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