Question

D is the sum of the odd numbers from 1 through 99 inclusive, and N is the sum of the even numbers from 2 to 98 inclusive.
D =1 + 3 + 5 + ... + 99 and N = 2 + 4 + 6 + ... 98
Which is greater D or N and by how much?
(The ... means all the other odd numbers for D and all the even numbers for N)

Answer 1

here is your answer....

Answer 2

D is greater than N by a difference of 50.

Both D and N are sum of two different A.P series.

For D (sum of odd numbers from 1 to 99) -

a = first term = 1

d = common difference = 2

n = number of terms = 50

Sum of the series = n/2 (2a + (n-1)d )

=> Sum = 2500

D = 2500

For N (sum of even numbers from 1 to 99) -

a = first term = 2

d = common difference = 2

n = number of terms = 49

Sum of the series = n/2 (2a + (n-1)d )

=> Sum = 2450

N = 2450

D is greater than N by a difference of 50.