Please explain how to find the pattern. Thanks.
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Question
Answer
BigDevil
| Pattern | No. of Sticks | |
| 1 | 4 | 4 × (1) + 0 |
| 2 | 13 | 4 × (1 + 2) + 1 |
| 3 | 26 | 4 × (1 + 2 + 3) + 2 |
| 4 | 43 | 4 × (1 + 2 + 3 + 4) + 3 |
| 5 | 64 | 4 × (1 + 2 + 3 + 4 + 5) + 4 |
| n | 4 × (1 + 2 + 3 +…..+ n) + (n – 1) |
Formula for (1 + 2 + 3 +…..+ n) is n(n + 1) /2
So formula for number of sticks is 4n(n + 1)/2 + (n – 1) or 2n(n + 1) + (n – 1)