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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?
• 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.
• Geometric Sequences An exercise on geometric sequences including finding the nth term and the sum of any number of terms.
• Geometric Sequences Video Revise all you need to know about geometric sequences and series.
• Venn Diagram of Sequences Find the formula for the nth term of sequences that belong in the given sets.
• Sequences Table Challenge Complete the table showing the terms of the sequences and the formulas for the nth terms.

Here are some exam-style questions on this statement:

• "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
• "In a geometric series the common ratio is \(r\) and sum to \(n\) terms is \(S_n\)." ... 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 sum of the first n terms of a geometric sequence is given by:" ... more

See all these questions

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
• 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.