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In a circular array of 2n numbers, the sum of any n consecutive numbers is always S. If the first number in the array is x, express the (n+1)th number in terms of x and S. A) S – x B) 2S – x C) S + x D) 2S + x
The correct answer is B) 2S - x. Since the sum of any n consecutive numbers is always S, we can write: x + x+1 + ... + x+n-1 = S ... (1) And, x+1 + x+2 + ... + x+n = S ... (2) Subtracting (1) from (2), we get: (x+n) - x = S - S x+n = 2S - x So,Read more
The correct answer is B) 2S – x.
Since the sum of any n consecutive numbers is always S, we can write:
x + x+1 + … + x+n-1 = S … (1)
And,
x+1 + x+2 + … + x+n = S … (2)
Subtracting (1) from (2), we get:
(x+n) – x = S – S
x+n = 2S – x
So, the (n+1)th number (x+n) is equal to 2S – x.
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