Please explain the first statement and solve it explicitly. thank you

The sum of k consecutive and positive integers in a sequence is S. If k is between 1 and 100, inclusive, what is the probability that \frac{S}{k} results in a value that is part of the sequence?

k = no. of integers in the series

s = sum of the numbers in series

s/k, therefore, is the average of the series

if k is an odd number for eg 3, the numbers would be:

n, n+1, n+2

s = 3n + 3

s/k = n + 1 , ie the 2nd term

You will find that for all odd numbers, the mean would be the middle number

For even k, for eg 4, the numbers would be:

n, n+1, n+2, n+3

s = 4n + 6

s/k = n + 1.5 , not a term

The probability terefore will be 0.5

1 Like

is this correct ?

since it is consecutive numbers. s/k is average, avg should lie in the series.

ie case 1: 1 to 5, avg is (1+5)/2=3 .

case 2: 1 to 4 , avg will be 2.5 so , if series is even length ,s/k wont be there, so its a 50/50

and answer was .5

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