DeeptiM wrote:
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
Pls help with the easiest explanation possible..thnx
Let's see the pattern:
For n=5, the sequence will be {1,2,3,4,5}
\(S(n)=S(5)=1+2+3+4+5\)
2n=2*5=10, the sequence will be {1,2,3,4,5,6,7,8,9,10}
\(S(2n)=S(10)=1+2+3+4+5+6+7+8+9+10=1+2+3+4+5+(1+5)+(2+5)+(3+5)+(4+5)+(5+5)\)
\((1+2+3+4+5)+(1+2+3+4+5)+(5+5+5+5+5)\)
\(S(5)+S(5)+5*5=S(5)+S(5)+5^2=2S(5)+5^2\)
Since, n=5
\(2S(5)+5^2=2S(n)+n^2\)
In general terms,
\(S(n)=1+2+3+4,...+n\)
\(S(2n)=1+2+3+4,...+n+(1+n)+(2+n)+(3+n)+(4+n),...+(n+n)\)
\(S(2n)=(1+2+3+4+...+n)+(1+2+3+4+...n)+(n+n+...n-times)\)
\(S(2n)=S(n)+S(n)+n^2\)
\(S(2n)=2S(n)+n^2\)
Ans: "D"