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GMAT - Problem Solving - Arithmetic

For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 301?

For any positive integer n, the sum of the first n positive integers equals n(n 1)/2. What is the sum of all the even integers between 99 and 301?

A. 10,100
B. 20,200
C. 22,650
D. 40,200
E. 45,150

We have to find out the sum : 100 + 102 + 104 + . . . + 300

= 2 (50 + 51 + 52 + . . . + 150)

{We can use sum of an Arithmetic progression formula, but for the sake of the question we can use the formula in the question}

= 2 (1 + 2 + 3 + . . . + 50 + 51+ . . . + 150 - (1 + 2 + 3 + . . . + 49))

= 2 (150*151/2  - 49*50/2)

= 150*151 - 49*50

= 20200

B is correct.