a) \(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+......+50+x=1275\)
\(\Rightarrow50x+\left(1+2+3+4+......+50\right)=1275\)
\(\Rightarrow50x+1221=1275\)
\(\Rightarrow50x=54\)
\(\Rightarrow x=\frac{27}{25}\)
b) \(x+2x+3x+.......+100x=10100\)
\(\Rightarrow x\left(1+2+3+.....+100\right)=10100\)
\(\Rightarrow5050x=10100\)
\(\Rightarrow x=2\)