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
−S=1+2+4+7+11...+n terms
−
0
=(1+1+2+3+4...n terms )−an
⇒an=1+{1+2+3+4...(n−1) terms } ⇒an=1+
n(n−1)
2
=
n2−n+2
2
.....(i)
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 .