3.2 Homework due 17.3.15 ANSWERS

1. Solve \[ \begin{align*} 3&x+2y=13 \\ -5&x+6y=81 \\ &\text{__________} \\ 15&x+10y=65 \\ -15&x+18y=243 \\ 28&y = 308 \\ \therefore &y=11 \\ &x=-3 \end{align*} \]

   [3 marks]

2. For the sequence $-3,2,7,12...$, find $u_n$ and $u_{50}$ \[ u_n=5n-8\\u_{50}=250-8=242 \]

   [3 marks]

3. For the sequence $24,21,18,15...$, find $u_n$ and $u_{50}$ \[ u_n=27-3n\\u_{50}=27-150=-123 \]

   [3 marks]

4. True or false, $-134$ is in the sequence $36,32,28,....$. Give a reason for your answer. \[ u_n=40-4n\\ 40-4n=-134 \\ -4n=-174 \\ n=43.5\] NOT in the sequence as n is not a whole number

   [2 marks]

5. Write down the first five terms of the sequence $u_n=12-5n$ \[ 7,2,-3,-8,-13 \]

   [2 marks]

6. How many green tiles would there be in pattern 120?
   \[ u_n=2n+1\\u_{120}=240+1=241 \]

   [2 marks]

7. Expand $(3x+2)(5x-4)$ \[15x^2-2x-8\]

   [2 marks]

8. Factorise $x^2-3x+28$ \[(x-7)(x+4)\]

   [2 marks]

9. Find $u_n$ for $-1,2,7,14,23,....$ \[u_n=n^2-2 \]

   [2 marks]

10. Find $u_n$ for $2,16,54,128,250....$ \[u_n = 2n^3 \]

    [2 marks]