Cookies are used on this website.

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

• Missing Terms Can you work out which numbers are missing from these number sequences?
• Leapfrog An investigation of the minimum number of moves required to make the blue and green frogs swap places.
• Matchstick Patterns Create a formula to describe the nth term of a sequence by examining the structure of the diagrams.
• Arithmetic Sequences An exercise on linear sequences including finding an expression for the nth term and the sum of n terms.
• Arithmetic Sequences Video A reminder of how to find the next term, the nth term and the sum of terms of an arithmetic or linear sequence.
• Handshakes If everyone in this room shook hands with each other, how many handshakes would there be?
• Venn Diagram of Sequences Find the formula for the nth term of sequences that belong in the given sets.
• Quadratic and Cubic Sequences Deduce expressions to calculate the nth term of quadratic and cubic sequences.
• Sequences Table Challenge Complete the table showing the terms of the sequences and the formulas for the nth terms.
• Parts of Sequences Find the formula that describes the part of the sequence that can be seen

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
• "In a sequence" ... more
• "This expression can be used to generate a sequence of numbers." ... more
• "Work out an expression for the n^th term of the quadratic sequence" ... more
• "Here are the first six terms of a quadratic sequence." ... more
• "Find an expression, in terms of \(n\), for the \(n\)th term of the sequence that has the following first five terms:" ... more
• "Here are the first six terms of a quadratic sequence." ... 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
• "A celebrity football match is planned to take place in a large stadium." ... more

See all these questions

Here is an Advanced Starter on this statement:

• 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.

• Sequences A pattern of numbers following a rule is called a sequence. There are many different types of sequence and this topic introduces pupils to some of them. The most basic sequences of numbers is formed by adding a constant to a term to get the next term of the sequence. This rule can be expressed as a linear equation and the terms of the sequence when plotted as a series of coordinates forms a straight line. More complex sequences are investigated where the rule is not a linear function. Other well-known sequences includes the Fibonacci sequence where the rule for obtaining the next term depends on the previous two terms. Sequences can be derived from shapes and patterns. A growing patterns of squares or triangles formed from toothpicks is often used to show linear sequences in a very practical way. Diagrams representing sequences provides interesting display material for the classroom. Typically pupils are challenged to find the next term of a given sequence but a deeper understanding is needed to find intermediate terms, 100th term or the nth term of a sequence.