Difference between the square of two consecutive integrers is 408235. Sum of the number is
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The difference between two consecutive squares is an ever increasing odd number.
So, the sequence 1, 4, 9, 16, 25, 36, 49, 64, 81 has difference between consecutive members is 3, 5, 7, 9, 11, 13, 15, 17.
81 - 64 is 17; therefore the number you are looking for is sqrt(81), or 9.
Anther way to get this is:
(n + 1) ^ 2 - n^ 2 = 17
n^2 + 2n + 1 - n^2 = 17
2n + 1 = 17
2n = 16
n = 8
So, if n = 8, then n+1, the larger number, = 9.
Finally, the general solution for problems of this form is: If the difference between two consecutive squares is N, then to get the smaller of the two numbers, subtract 1 from N and … (more)
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yesh
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