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Question
(i) Draw the next pattern
(ii) Prepare a table for the number of dots used for each pattern
(iii) Explain the pattern
(iv) Find the number of dots in the 25th pattern
Solution
(i) The next pattern is
(ii)
| Pattern Number | 1 | 2 | 3 | 4 | 5 |
| Number of dots | 2 | 5 | 9 | 14 | 20 |
(iii)
| Pattern | Number of dots |
| 1 | 2 |
| 2 | 2 + 3 |
| 3 | 2 + 3 + 4 |
| 4 | 2 + 3 + 4 + 5 |
First number is 2
2nd number is 2 + 3 = 5
3rd number is 5 + 4 = 9
4th number is 9 + 5 = 14
5th number is 14 + 6 = 20
(iv) Number of dots in the 25th pattern is
| Pattern | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 |
| No. of dots | 2 | 5 | 9 | 14 | 20 | 27 | 35 | 44 | 54 | 65 | 77 | 90 | 104 | 119 | 135 | 152 | 170 | 189 | 209 | 230 | 252 | 275 | 299 | 324 | 350 |
The number of dots in the 25th pattern = 350.
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