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NSW Y8 Maths

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NSW Y8 Maths Graphing Linear Equations Finding Rules for Number Patterns

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Finding Rules for Number Patterns Theory

\begin{multicols}{2} \textbf{Example 1}\\ Find the pronumerals in the number pattern: $$ 1,3,5,7, a, b $$ \textbf{Example 1 solution}\\ The numbers are increasing by 2\\ \(\begin{aligned} \therefore a & =7+2=9 \\ b & =a+2=11 \end{aligned}\) \vfill \columnbreak \textbf{Example 2}\\ Find the formula for the \(n\)th term \(T_n\) of the pattern \(10,7,4,1,\dots\) and hence find the 10th term \(T_{10}\), given that \(T_1=10\).\\ \textbf{Example 2 solution}\\ \(T_n=m n+b\)\\ when \(n=1,\; T_1=10\)\\ \(\therefore 10=m+b\)\\ The terms are decreasing by 3\\ \(\begin{aligned} \therefore m & =-3 . \\ \therefore 10 & =-3+b \\ b & =13 \\ \therefore T_n & =-3 n+13 \\ T_{10} & =-3\times 10+13 \\ \therefore T_{10} & =-17 \end{aligned}\) \end{multicols}

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  • Finding Rules for Number Patterns - Video - Making an algebraic rule from a simple pattern

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