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

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New post 26 Aug 2018, 06:17
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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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For each integer n > 1, if S(n) denote the sum of even integer upto  [#permalink]

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New post 26 Aug 2018, 06:26
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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Re: For each integer n > 1, if S(n) denote the sum of even integer upto  [#permalink]

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New post 26 Aug 2018, 11:30
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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Re: For each integer n > 1, if S(n) denote the sum of even integer upto  [#permalink]

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New post 26 Aug 2018, 12:22
PKN , what do you mean by AP ?
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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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New post 26 Aug 2018, 12:46
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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New post 26 Aug 2018, 20:01
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 &nbs [#permalink] 26 Aug 2018, 20:01
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