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Students learn how to generate and describe arithmetic and geometric sequences on a position-to-term basis. Learning progresses from plotting and reading coordinates in the first quadrant to describing geometric sequences using the nth term.

This unit takes place in Term 4 of Year 10 and is followed by the equations of straight line graphs.

- Use simple formulae
- Generate and describe linear number sequences
- Express missing number problems algebraically

- Pupils need to be able to use symbols and letters to represent variables and unknowns in mathematical situations that they already understand, such as:
- missing numbers, lengths, coordinates and angles
- formulae in mathematics and science
- equivalent expressions (for example, a + b = b + a)
- generalisations of number patterns

- Generate terms of a sequence from either a term-to-term or a position-to-term rule
- Recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences, and simple geometric progressions ( r<sup<n where n is an integer, and r is a rational number > 0 or a surd) and other sequences
- Deduce expressions to calculate the nth term of linear and quadratic sequences

- The nth term represents a formula to calculate any term a sequence given its position.
- To describe a sequence it is important to consider the differences between each term as this determines the type of pattern.
- Quadratic sequences have a constant second difference. Linear sequences have a constant first difference.
- Geometric sequences share common multiplying factor rather than common difference.
- Whereas a geometric and arithmetic sequence depends on the position of the number in the sequence a recurrence relation depends on the preceding terms.

- Students often show a lack of understanding for what ‘n’ represents.
- A sequence such as 1, 4, 7, 10 is often described as n + 3 rather than 3n – 2.
- Quadratic sequences can involve a linear as well as a quadratic component.
- Calculating the product of negative numbers when producing a table of results can lead to difficulty.
- The nth term for a geometric sequence is in the form ar
^{n-1}rather than ar^{n}. - Students often struggle understanding the notation of recurrence sequences. In particular, using difference values of n for a given term.

September 10, 2018

An equation is when one expression, or term, is equal to another. To solve an equation means to find the value of the variable (represented by a letter) that makes the two expressions equal. There are two types of equations for secondary school mathematics, linear and none-linear. In this blog I write about how I […]

August 4, 2018

When learning how to simplify surds students need to understand the difference between a rational and irrational number. Rational numbers include integers and terminating and repeating decimals. They can be written as a fraction with both the numerator and denominator as integers. An irrational number is a number which, in its decimal form does not […]

July 9, 2018

There are three common methods for sharing an amount to a given ratio. Depending on the age group and ability range I am teaching I would choose one approach over the other two. The three methods are: Using fractions Unitary method Using a table In this blog I will demonstrate each of the three methods […]