self Maths Puzzle

What is the relationship between the 3 sequences given by:
S1: 1,5,14,30... S2: 5,17,35,59...
S3: 1,17,98,354...

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self Other Question

In the word RAINBOW how many words are there in which A is always before I and I is always before O?
a)840
b)420
c)720
d)none of these

please explain the method clearly 10=10
-10=-10
1-11=100-110
adding(11/2)^2
1-11+(11/2)^2=100-110+(11/2)^2
(1)^2-2*11/2*1+(11/2)^2=(10)^2-2*11/2*10+(11/2)^2
using identity
(a-b)^2=a^2+b^2-2ab
(1-11/2)^2=(10-11/2)^2
1-11/2=10-11/2
1=10

it is wrong or right
if it is wrong then why?