100^2 - 99^2 + 98^2 - 97^2 + 96^2 - 95^2 + ... + 2^2 - 1^2 = ?

Question

Which set of numbers would most logically fill in the blanks in the following series?
101, 99, 102, 98, 103, 97, _ , _ ,105, 95, 104, 94
(a) 101 98
(b) 104 96
(c) 106 99
(d) none of these

Please provide your reasoning also?

Answer 1

By this Formula (a+1)^2 - a^2 = 2a + 1 = (a+1) + a

so
100^2-99^2 = 100+ 99
98^2 - 97 ^2 = 98+97
96^2-95^2 = 96 + 95

so on
adding we get 100^2-99^2+98^2-97^2+...+2^2-1^2 =100 + 99 + 98 ... + 1 = sum of integers from 1 to 100 = 100 *101/2 = 5050