Let x represent the sum of the first 25 positive odd integers. Let y represent the sum of the next 25 positive odd integers. What is the value of y - x?
x = 1 , 3 , 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 27 , 29 , 31 , 33 , 35 , 37 , 39 , 41 , 43 , 45 , 47 , 49 , Total = 625
y = 51 , 53 , 55 , 57 , 59 , 61 , 63 , 65 , 67 , 69 , 71 , 73 , 75 , 77 , 79 , 81 , 83 , 85 , 87 , 89 , 91 , 93 , 95 , 97 , 99 , Total = 1875
y - x =1875 - 625 =1,250
+15001 Let x represent the sum of the first 25 positive odd integers. Let y represent the sum of the next 25 positive odd integers. What is the value of y - x?
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\(X=\sum(1,3,5...45,47,49)=25\cdot\frac{1+49}{2}=625\\ Y=\sum(27,29,31...45,47,49)=25\cdot\frac{51+99}{2}=1875\)
\(Y-X=1875-625=1250\)
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