For each integer n 1, if S(n) denote the sum of even integer upto

Question

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

aghosh54 · Answer

Using the formula Sum of first n even integer = n(n+1)
Here n=300/2=150
So sum is 150*151=22650
So S(300)=22650-300=22350

PKN · Answer

To find:- 2+4+6+---+298
No of terms of the series= \frac{298-2}{2}+1 =148+1=149

Sum of n terms of an AP when 1st and last term is known:
 \frac{n}{2}*(1st_term+Last_term)=\frac{149}{2}*(2+298)=\frac{149}{2}*300=149*150=22350

Ans. (B)

magbot · Answer

PKN , what do you mean by AP ?

aghosh54 · Answer

2+(2+2)+(4+2)+(6+2)+..... and so on
So you can see that the sequence is in Arithmetic Progression, which means every term is at distance of d=2 from its previous term.

PKN · Answer

Hi magbot , The acronym AP stands for Arithmetic Progression. More about AP, https://gmatclub.com/forum/math-sequenc ... 01891.html Note:- Above link is a part of GMAT club Math book. Posted from my mobile device

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For each integer n > 1, if S(n) denote the sum of even integer upto

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