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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.
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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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