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 $25^{th}$ pattern
(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 $25^{th}$ pattern
✓
Answer
(i) The next pattern is
(ii)
(iii)
First number is 2
$2^{nd}$ number is 2 + 3 = 5
$3^{rd}$ number is 5 + 4 = 9
$|4^{th}$ number is 9 + 5 = 14
$5^{th}$ number is 14 + 6 = 20(iv) Number of dots in the $25^{th}$ pattern is
The number of dots in the $25^{th}$ pattern = 350.
(ii)
| Pattern Number | 1 | 2 | 3 | 4 | 5 |
| Number of dots | 2 | 5 | 9 | 14 | 20 |
| Pattern | Number of dots |
| 1 | 2 |
| 2 | 2 + 3 |
| 3 | 2 + 3 + 4 |
| 4 | 2 + 3 + 4 + 5 |
$2^{nd}$ number is 2 + 3 = 5
$3^{rd}$ number is 5 + 4 = 9
$|4^{th}$ number is 9 + 5 = 14
$5^{th}$ number is 14 + 6 = 20(iv) Number of dots in the $25^{th}$ 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 |
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