mathematics

Philippines
March 17, 2007 8:09am CST
1,2,2,3,3,3,4,4,4,4,5,5,5,5,5... find the 100th term.. the faster the better..
3 responses
• China
8 May 07
It's very easy. a1=1+1*0,a2=2=a1+1*1,a3=a1+1*2,……an=a1+1*(n-1)=n n=? a1+a2+a3+……an=100 =a1+a1+1+a1+2+a1+3+……a1+n-1 =n*a1+0+1+2+3+……+n-1 =n*1+(0+n-1)*n/2 (a1=1) =100 so n+n^2/2-n/2=n^2/2+n/2=100 turning chien gets n^2+n=200 (n^2+n-200=0) result: 14 formula: n^2/2+n/2- the 100th term=0
@rodmac (94)
4 May 07
100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100 {100 repeated side by side for a total of 100 times - BIG}
@Asylum (48273)
• Manchester, England
17 Mar 07
The 100th figure should be 14. This is a simple matter of adding 1+2+3+4 etcetera until you reach the figure of 100, which would actually be surpassed by 14.