Mathematics - Sequence & Series Question with Solution | TestHub

$\begin{array}{rl}& \mathrm{n}(3)\Rightarrow \text{ multiple of }3\\ & 102,105,108,\dots ..,699\\ & {\mathrm{T}}_{\mathrm{n}}=699=102+(\mathrm{n}-1)(3)\\ & \mathrm{n}=200\\ & \mathrm{n}(3)=200\\ & \because \mathrm{n}(4)\Rightarrow \text{ multiple of }4\end{array}$ $\begin{array}{rl}& 100,104,108,\dots .,700\\ & T_n=700=100+(n-1)(4)\\ & n=151\\ & n(4)=151\\ & n(3\cap 4)\Rightarrow \text{ multiple of }3\&4\text{ both }\\ & 108,120,132,\dots .,696\\ & T_n=696=108+(n-1)(12)\\ & n=50\\ & n(3\cap 4)=50\\ & n(3\cup 4)=n(3)+n(4)-n(3\cap 4)\\ & =200+151-50\\ & =301\\ & n(\overline{3\cup 4})=\text{ Total }-n(3\cup 4)=\text{ neither a multiple }\\ & \text{ of }3\text{ nor a multiple of }4\\ & =601-301=300\end{array}$