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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.

April 15, 2018

Inspiring students to enjoy maths and feel the success that comes with attempting a difficult challenge is why I teach. The feeling of success is addictive. The more students experience it the more they want it and the further out of their comfort zone they are willing to go to get more of it. Teaching […]

April 11, 2018

To find the equation of straight line graphs students need to calculate the gradient using two pairs of coordinates and the intercept which is the y value of where it crosses the vertical axis. Examiner’s reports of past exam questions show students are more able to find the intercept of a straight line than they […]

March 23, 2018

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. Arithmetic […]