Question 1204069
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Consecutive numbers follow one right after another. 
An example would be 7,8,9.


A,B,C are consecutive natural numbers from the set {1,2,3,4,...}


Since B follows right after A, we can state: B = A+1
Also C = B+1 = (A+1)+1 = A+2


The sequence A, B, C is the same as A, A+1, A+2.


(2/7)*(reciprocal of A) = (1/3)*(reciprocal of C)
(2/7)*(1/A) = (1/3)*(1/C)
2/(7A) = (1/3)*(1/(A+2))
2/(7A) = 1/(3(A+2))
2*3(A+2) = 7A*1 .... cross multiplication
6A+12 = 7A
12 = 7A-6A
12 = A
A = 12


If A = 12, then,
B = A+1 = 12+1 = 13
C = A+2 = 12+2 = 14


In short
A = 12
<font color=red>B = 13</font>
C = 14


Let's check to see if we have the right answer.
(2/7) of (1/A) = (1/3) of (1/C)
(2/7)*(1/12) = (1/3)*(1/14)
(2*1)/(7*12) = (1*1)/(3*14)
(2*1)/(7*2*6) = (1*1)/(3*14)
1/42 = 1/42
We have confirmed the answer is correct.


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Answer: <font color=red size=4>B = 13</font>
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