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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
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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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