If S(n) is the sum of sequence

[mehrak]

If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of n and S(n), S(2n)=?
(A) 2*S(n)
(B) n*S(n)
(C) 2n*S(n)
(D) 2S(n)+n^2
(E) S(n)+2n^2

SPOILER:
OA: D

[e.cartman]

S(n)=n(n+1)/2
S(2n) = 2n(2n+1)/2 = n(2n+1) = n^2+n(n+1) = n^2+2S(n).
So D.

[queen2]

Originally Posted by e.cartman

S(n)=n(n+1)/2
S(2n) = 2n(2n+1)/2 = n(2n+1) = n^2+n(n+1) = n^2+2S(n).
So D.

excellent explanation e.cartman!

[aseemrules]

For those who dont remember the formula:

Put n=3 and check the choices. Only D fits in. Hit and Trial

[Gmater-1]

Originally Posted by e.cartman

S(n)=n(n+1)/2
S(2n) = 2n(2n+1)/2 = n(2n+1) = n^2+n(n+1) = n^2+2S(n).
So D.

cartman, could you please explain it further how you arrived at

n(2n+1) = n^2+n(n+1) = n^2+2S(n)

[swethapv]

The sum of an arithmetic series is given by the formula:
n(a1 + an)/2
Where, n is the number of numbers in the series
a1 is the 1st number in the series
an is the last number of the series
Now we can find an by the formula:
an = a1 + (n-1)d
where d is the difference between two consecutive numbers in the series
therefore, our sum formula becomes (by replacing an):
S(n) = n[2a1 + (n-1)d]/2
Now in the given series,
a1 = 1
d = 1
hence the equation becomes:
S(n) = n[2 + n-1]/2 = n(n+1)/2 =(n^2 + n)/2
therefore S(2n) = 2n^2 + n
so check each of the choices to see which one of them yields the above equation. Only choice D satisfies the above equation.

[vinhan]

Originally Posted by Gmater-1

cartman, could you please explain it further how you arrived at

n(2n+1) = n^2+n(n+1) = n^2+2S(n)

sum of n terms = n(n+1)/2

we need to find S(2n). put 2n in place of n

S(2n) = 2n(2n+1)
hence D is the answer

[Gmater-1]

Originally Posted by vinhan

sum of n terms = n(n+1)/2

we need to find S(2n). put 2n in place of n

S(2n) = 2n(2n+1)
hence D is the answer

Still not clear "2n(2n+1)" is not in any of the answer choices

[gmatissimple]

S(n) =n(n+1)/2
So, S(2n) =2n(2n+1)/2 =2n^2+n =n^2+n^2+n =n^2+n(n+1)
=n^2+2n(n+1)/2 [Multiplying and diving by 2]
=n^2+2S(n) [As S(n)=n(n+1)/2]
Answer: n^2+2S(n)

[nightbreeze]

Originally Posted by Gmater-1

Still not clear "2n(2n+1)" is not in any of the answer choices

That would be too easy...they like to make the process simple enough so that you can arrive to the solution, but then have to pass through five pains in order to understand which of the answers, transformed, is equal to it.