Question
The diagram shows patterns of white and grey squares.
| Diagram | Number of grey squares (G) | Number of white squares (W) | Total number of squares (Q) |
| 1 | 1 | 0 | 1 |
| 2 | 1 | 8 | 9 |
| 3 | 17 | 8 | 25 |
| 4 | 17 | 32 | 49 |
| 5 | … | … | … |
| 6 | 49 | p | q |
(a) Find the values of p and q. [2]
(b) (i) Write down an expression, in terms of n, for the total number of squares (Q) for Diagram n. [1]
(ii) Explain why it is not possible to have a diagram with a total of 226 squares. [1]
(c) Write an equation connecting G, W and Q. [1]
(d) If there are 161 grey squares in Diagram 10, calculate the number of white squares. [2]
Solution
