KEAM 2013 Math Paper

Given sequence is 1,2,2,3,3,3,4,4,4,4,...
First term =1
Second term =2
Fourth term =3
Seventh term =4
Eleventh term =5..., so on
∴ Let S=1+2+4+7+11...n terms
If n=14, then an=92
i.e., 92nd term is 14 .
If n=15, then an=106
i.e., 106 th term is 15 .
Hence, 100 th term is 14 .