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When you subtract one square number from the next higher square what is the difference?
Wiki User
∙ 6y ago
The difference is an odd number (2n+1), as shown from (n+1)² = n² + 2n + 1, which as you can see is a linear progression of odd numbers, either n or (n+1) being odd.
4-1 = 3
9-4 = 5
16-9 = 7
25-16 = 9
36-25 = 11
49-36 = 13
64-49 = 15
81-64 = 17
The difference between any two ODD squares is always a multiple of 8, where for an odd n, and odd n+2, the difference in their squares is the sum of the two intervening differences, and can be expressed as 4n+4.
1) 9-1 = 8
3) 25- 9 = 16
5) 49-25 = 24
7) 81-49 = 32
Wiki User
∙ 6y ago
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