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These are the Transum resources related to the statement: "Geometric sequences and series. Use of the formulae for the nth term and the sum of the first n terms of the sequence. Use of sigma notation for the sums of geometric sequences".

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

- Geometric Sequences An exercise on geometric sequences including finding the nth term and the sum of any number of terms.
- Parts of Sequences Find the formula that describes the part of the sequence that can be seen
- Sigma Practise using the sigma notation to find the sum of various number series.

Here are some exam-style questions on this statement:

- "
*The diagrams above show a growing fractal of triangles. The sides of the largest equilateral triangle in each diagram are of length 1 metre.*" ... more - "
*A square is drawn with sides of length 32 cm. The midpoints of the sides of this square are joined to form a new square and four red triangles. The process is repeated to produce yellow triangles and then again to produce blue triangles.*" ... more - "
*The first term of an infinite geometric sequence is 10. The sum of the infinite sequence is 500.*" ... more - "
*Chris checks his Twitter account and notices that he received a tweet at 8:00am. At 8:05am he forwards the tweet to four people. Five minutes later, those four people each forward the tweet to four new people. Assume this pattern continues and each time the tweet is sent to people who have not received it before.*" ... more - "
*The following is an arithmetic sequence: \( \log_7 8 \text{, } \log_7 a \text{, } \log_7 b \text{, } \log_7 64 \) where \(a \gt 1 \text{ and } b \gt 1\)*" ... more - "
*(a) Expand the following as the sum of six terms:*" ... more - "
*Consider the number sequence where \(u_1=500, u_2=519, u_3=538\) and \(u_4=557\) etc.*" ... more

Here are some Advanced Starters on this statement:

**Grandmother**

How far would grandma have travelled after a suitably large number of days given her walking regime? more**Rice on a Chess Board**

How many grains of rice are on a chess board if each square has twice the number of grains as the previous square. more**Same Series Sum**

Find an arithmetic series and a geometric series that have the same sum of the first five terms. more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

If you use a TI-Nspire GDC there are instructions here for generating a sequence on the calculator.

This video on Geometric Sequences is from Revision Village and is aimed at students taking the IB Maths Standard level course.

How do you teach this topic? Do you have any tips or suggestions for other teachers? It is always useful to receive feedback and helps make these free resources even more useful for Maths teachers anywhere in the world. Click here to enter your comments.