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These are the Transum resources related to the statement: "Work with sequences including those given by a formula for the n^{th} term and those generated by a simple relation of the form x_{n+1} = f(x_{n}); increasing sequences; decreasing sequences; periodic sequences".

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

- Arithmetic Sequences An exercise on linear sequences including finding an expression for the nth term and the sum of n terms.
- Aunt Lucy's Legacy Decide which of the four schemes Aunt Lucy proposes will provide the most money. This investigation involves the sum of sequences as well as considering life expectancy.
- Fibonacci Quest A number of self marking quizzes based on the fascinating Fibonacci Sequence.
- Geometric Sequences An exercise on geometric sequences including finding the nth term and the sum of any number of terms.
- Missing Terms Can you work out which numbers are missing from these number sequences?
- Quadratic and Cubic Sequences Deduce expressions to calculate the nth term of quadratic and cubic sequences.

Here are some exam-style questions on this statement:

- "
*The first five terms of an arithmetic sequence are:*" ... more - "
*Here is a picture of four models. Some of the cubes are hidden behind other cubes.*" ... more - "
*(a) Find the \(n\)th term of the sequence 7, 13, 19, 25,...*" ... more - "
*Consider the number sequence where \(u_1=500, u_2=519, u_3=538\) and \(u_4=557\) etc.*" ... more - "
*Find an expression, in terms of \(n\), for the \(n\)th term of the sequence that has the following first five terms:*" ... more - "
*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 - "
*The diagrams below show a sequence of patterns made from red and yellow tiles.*" ... more - "
*The first three and last terms of an arithmetic sequence are \(7,13,19,...,1357\)*" ... more - "
*An arithmetic sequence is given by 6, 13, 20, …*" ... more - "
*In an arithmetic sequence, the fifth term is 44 and the ninth term is 80.*" ... 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 - "
*A celebrity football match is planned to take place in a large stadium.*" ... more - "
*A Grecian amphitheatre was built in the form of a horseshoe and has 22 rows.*" ... 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 sums of the terms of a sequence are given as follows where \(k\in \mathbb{Z}\):*" ... more

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

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