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
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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❎Level 1  Find the next term of these geometric sequences
Level 2  Find a given term of these geometric sequences
Level 3  Mixed questions about geometric sequences and their sums
Level 4  Sum of infinite convergent geometric sequences
Missing Terms  Find the missing terms of arithmetic, geometric and Fibonaccitype sequences in this self marking quiz.
Exam Style questions are in the style of GCSE or IB/Alevel 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 u_{1}
The n^{th} term of the sequence can be written as u_{n}
The common ratio is usually written as r
The formula for finding the n^{th} term is u_{n}=u_{1}r^{(n1)}
The excellent video above is from Corbettmaths.
The formula for finding the sum of \(n\) terms is:
$$ S_n = \dfrac{u_1(r^n1)}{r1}$$The sum of an infinite geometric sequence is:
$$ S_\infty = \dfrac{u_1}{1r}, \quad r \lt 1 $$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 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.
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