CAT 2023 Slot 3 Solved Paper

The first series goes as follows:
$46,54,62,70,78,86,94,102,....$
The second series goes as follows:
$98,102,106,110,...$
The first common term is 102 (first term of the common terms) and the common difference between them will be $\mathrm{hcf}\left(4,8\right)=8$
⇒ The required sequence is $102,110,118,....$. (last term should be less than 468 (100th term of second series))
$\Rightarrow 102+\left(\mathit{n}-1\right)\left(8\right)\le 498$
$\Rightarrow \mathit{n}$ is less than or equal to $50.5\Rightarrow \mathit{n}=50$
Using the summation of A.P. formula:
Required sum