Worked Example 1: Tile Pattern

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Worked 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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