SOLUTION: What is the smallest natural # that is simultaneously the sum of 9,10, & 11 consecutive integers?

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Question 931028: What is the smallest natural # that is simultaneously the sum of 9,10, & 11 consecutive integers?
Answer by ptfile(81) About Me  (Show Source):
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Let a1 = 1
d = 1
Sn = n/2(2a1+(n-1)d)
Sn = n/2(a1+an)
sum of 9
Sn = n/2(a1+an)
Sn = 9/2(1+9)
Sn = 9/2(10)
Sn = 45
Sum of 10
Sn = n/2(a1+an)
Sn = 10/2(1+10)
Sn = 5(11)
Sn = 55
Sum of 11
Sn = n/2(a1+an)
Sn = 11/2(1+11)
Sn = 11/2(12)
Sn = 66
45+55+66=166
The number is 166.