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Quiz yourself on Quadratic SequencesGet your flashcardsBuild my revision planTrack my progressWorked Example 1: Tile Pattern
Problem: Find the nth term of the sequence 2, 5, 10, 17, 26, ...
Step 1: First differences
| Terms: | 2 | 5 | 10 | 17 | 26 |
| 1st differences: | 3 | 5 | 7 | 9 |
Step 2: Second differences
| 1st differences: | 3 | 5 | 7 | 9 |
| 2nd differences: | 2 | 2 | 2 |
Step 3: Find 'a'
a = ½ × 2 = 1, so we have n²
Step 4: Compare with n²
| n: | 1 | 2 | 3 | 4 | 5 |
| Original: | 2 | 5 | 10 | 17 | 26 |
| n²: | 1 | 4 | 9 | 16 | 25 |
| Difference: | 1 | 1 | 1 | 1 | 1 |
Step 5: Complete formula
The difference is constant = 1, so the formula is:
nth term = n² + 1
Check: When n = 3: 3² + 1 = 9 + 1 = 10 ✓
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