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Math Expert V
Joined: 02 Sep 2009
Posts: 58453
For each integer n > 1, if S(n) denote the sum of even integer upto  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 65% (01:53) correct 35% (02:12) wrong based on 105 sessions

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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) $$90300$$

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Imperial College Moderator S
Joined: 16 May 2017
Posts: 98
Location: India
GMAT 1: 710 Q47 V39 WE: General Management (Retail Banking)
For each integer n > 1, if S(n) denote the sum of even integer upto  [#permalink]

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Bunuel 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) $$90300$$

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
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Joined: 01 Oct 2017
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Re: For each integer n > 1, if S(n) denote the sum of even integer upto  [#permalink]

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Bunuel 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) $$90300$$

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)
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Intern  B
Joined: 02 Sep 2015
Posts: 41
Re: For each integer n > 1, if S(n) denote the sum of even integer upto  [#permalink]

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PKN , what do you mean by AP ?
Imperial College Moderator S
Joined: 16 May 2017
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Location: India
GMAT 1: 710 Q47 V39 WE: General Management (Retail Banking)
Re: For each integer n > 1, if S(n) denote the sum of even integer upto  [#permalink]

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magbot wrote:
PKN , what do you mean by AP ?

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.
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Re: For each integer n > 1, if S(n) denote the sum of even integer upto  [#permalink]

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magbot wrote:
PKN , what do you mean by AP ?

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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Re: For each integer n > 1, if S(n) denote the sum of even integer upto  [#permalink]

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_________________ Re: For each integer n > 1, if S(n) denote the sum of even integer upto   [#permalink] 03 Sep 2019, 07:32
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