Let \(A\) be the set of first \(101\) terms of an A.P., whose first term is \(1\) and the common difference is \(5\) and…

First A.P.

Set \(\mathrm{A}=\{1,6,11,16 \ldots .101\) terms \(\}\)

Second A.P.
Set \(\mathrm{B}=\{9,16 \ldots . .71\) terms \(\}\)
\(\mathrm{D}=\mathrm{L} . \mathrm{C} . \mathrm{M}\left\{\mathrm{d}_1, \mathrm{~d}_2\right\}=35\)
\(1^{\text {st }}\) Common term is \(16\)
\(16+(\mathrm{n}-1) 35 \leq 499\)
\(\mathrm{n} \leq 14.8\)
\(\Rightarrow \mathrm{n}=14\)
\(A \cap B=\{16,51,86,121,156,191,226,261,296,331,366,401,436,471\}\)
Terms divisible by \(3=\{51,156,261,366,471\}\)
\(=5\) terms