1. Linear equations
[ A2.2 Extension Plenary]
A formula for sequences that have the same difference d between each term is Where is the nth term of the sequence whose first term is a. So for the sequence A = 5, d = 3 and etc. The 3rd term of a sequence, with constant difference between terms, is 13 and the 9th term is 43. Show how to use simultaneous equations to find the 100th term.
Explain carefully how to use simultaneous equations to find the equation of the straight line passing through the points (4, 3) and (3, 0).
Some parabolas have the general formula Where a and b are the same (called constants) for a particular parabola. A parabola goes through the points (1, 5) and (2, 14). Find the values of a and b for this parabola.
Preamble
These activities involve using simultaneous equations in a context. Representing
situations in a simultaneous equation format is found challenging. The situations re-
visit sequence and equations of straight lines. Question 2 requires an explanation – this
may be demonstrated by a small group to the greater group.
Possible content
Solving pairs of simultaneous equations by an algebraic method in a problem solving context.
Resources
None
Solution/Notes
The two equations are: a + 2d = 13 and a + 8d = 43, so d = 5 and a = 3. Giving the value of the 100th term as 498 (=  5)
Pupils own explanation based on substituting (4, 3) and (3, 0) into y = mx + c. Giving equations 3 = 4m + c and 0 = 3m + c, with m = 3 and c = -9 so the straight line equation is y = 3x – 9.
Substituting in the values of x and y for the two points gives: 5 = a + b and 14 = 4a + b giving a = 3 and b = 2 so y = 3x² + 2.
Original Material © Cambridge University Press 2010
Original Material © Cambridge University Press 2010