Mathematics - Sequence & Series Question with Solution | TestHub

$\begin{array}{rl}& A=\{1,6,11,16,21,26,31,36,41,46,51,56,61,\\ & 66,71,76,81,86,91,\dots \dots \}\\ & B=\{9,16,23,30,37,44,51,58,65,72,79,86,\\ & 93,100,\dots \dots \}\\ & A\cap B=\{16,51,86,\dots \dots \}\\ & \text{ For set ’A’ }\Rightarrow T_{2025}=1+(2025-1)(5)=10121\\ & \text{ For set ’ }{B}^{\prime }\Rightarrow T_{2025}=9+(2025-1)(7)=14177\\ & \text{ So, for }(A\cap B)\Rightarrow T_n=16+(n-1)(35)\le 10121\\ & (n-1)\le \frac{10121-16}{35}=288.71\\ & n\le 289.71\Rightarrow n=289\\ & \therefore n(A\cup B)=n(A)+n(B)-n(A\cap B)\\ & =2025+2025-289=3761\end{array}$