Answer: 13
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Step-by-step explanation:
The set of natural numbers is {1,2,3,4,...} aka the set of positive whole numbers.
Consecutive natural numbers follow one right after another, like with that example above or something like 7,8,9,...
Since B follows right after A, this means B = A+1. Similarly, C = B+1 = (A+1)+1 = A+2 because C follows right after B.
So we have
- A = some unknown natural number
- B = A+1
- C = A+2
In other words, we have the sequence A,A+1,A+2 to replace the sequence A,B,C in that order.
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The reciprocal of A is 1/A. Taking 2/7 of this gets us 2/(7A). This result is equal to 1/3 of the reciprocal of C, so,
2/(7A) = 1/3 of 1/C
2/(7A) = 1/(3C)
2/(7A) = 1/(3(A+2))
2/(7A) = 1/(3A+6)
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Let's cross multiply and solve for A
2/(7A) = 1/(3A+6)
2(3A+6) = 7A*1
6A+12 = 7A
12 = 7A-6A
12 = A
A = 12
Therefore, B = A+1 = 12+1 = 13 and C = A+2 = 12+2 = 14
The sequence A,B,C updates to 12,13,14.
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Check:
A = 12
reciprocal of A = 1/A = 1/12
D = 2/7 of reciprocal of A = (2/7)*(1/12) = 2/84 = 1/42
C = 14
reciprocal of C = 1/C = 1/14
E = 1/3 of the reciprocal of C = (1/3)*(1/14) = 1/42
Items D and E are equal, so it confirms we have the correct answer.