sandy wrote:

For each integer \(n>1\), if S(n) denote the sum of even integer upto \(n\) (not inclusive of \(n\)). For example, \(S(10)= 2+4+6+8=20\). What is value of \(S(300)\)?

(A) \(22050\)

(B) \(22350\)

(C) \(22650\)

(D) \(45150\)

(E) \(90300\)

there are three ways to do it ....

(I) If you know that Sum of first n integers is \(\frac{n(n+1)}{2}\)

Sum = \(2+4+6+...+300) = 2(1+2+3....+150)= 2 *\frac{150*151}{2}=150*151=22650\)

(II) If you know that Sum of first n integers is \(\frac{n(n+1)[}{fraction]\)

Now we have \([fraction]300/2}=150\) terms till 300, inclusive.

Sum = \(2+4+6+...+300 = 150*151=150*151=22650\)

(III) since it is an AP. the sum will be equal to Number of integers* average

so \(150 * \frac{(300+2)}{2} = 150*151 = 22650\)

C

To know more about Arithmetic progressions

https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
_________________

Some useful Theory.

1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048

2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825

3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html

4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html

5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html