BECE Mathematics 2013 Paper

Finding the rule of a mappingNote: If the mapping has equal interval (difference) for the $y$ and $x$ interval of 1 , you can use the general linear sequence formula to find the rule of the mapping.$U_n=U_1+(n-1)d$In the mapping, $U_n=y$ and $n=x$ and $U_1$, the first value of $y$$\;U_1=5$$\;y=5+(x-1)d$The $d$ is the interval between each consecutive $y$In this mapping, $d=8-5=11-8=14-11=17-14=3$We can substitute our $d$ and simplify the expression for $y$ $\;y=5+(x-1)d$$\;y=5+(x-1)3$$\;y=5+3 \times x-1 \times 3$$\;y=5+3x-3$$\;y=5-3+3x$$\;y=2+3x$$\;y=3x+2$$\;y \longrightarrow 3x+2$