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
Nibedita DuttaBegginer
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.