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Question
Observe the toothpick pattern given below:
(a) Imagine that this pattern continues. Complete the table to show the number of toothpicks in the first six terms.
| Pattern | 1 | 2 | 3 | 4 | 5 | 6 |
| Toothpicks | 4 | 13 |
(b) Make a graph by taking the pattern numbers on the horizontal axis and the number of toothpicks on the vertical axis. Make the horizontal axis from 0 to 10 and the vertical axis from 0 to 30.
(c) Use your graph to predict the number of toothpicks in patterns 7 and 8. Check your answers by actually drawing them.
(d) Would it make sense to join the points on this graph? Explain.
Solution
(a) On the basis of given patterns, we can arrange the following table which show the number of toothpicks in the first six terms.
| Pattern | 1 | 2 | 3 | 4 | 5 | 6 |
| Toothpicks | 4 | 7 | 10 | 13 | 16 | 19 |
Pattern and toothpicks shows the following relation as
1 → 4, 2 → 4 + 3 = 7
3 → 7 + 3 = 10, 4 → 10 + 3 = 13
5 → 13 + 3 = 16, 6 → 16 + 3 = 19
(b) On the basis of given condition, we can draw the following graph
(c) The graph follows the y = 3x + 1 pattern. If x = 7, then y = 3 × 7 + 1 = 21 + 1 = 22 and if x = 8, then y = 3 × 8 + 1 = 24 + 1 = 25.
| x | 7 | 8 |
| y | 22 | 25 |
(d) Yes, it shows the relation between x and y follows the given pattern y = 3x + 1.
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