2025 CGSS PRELIMS P1 Q13

Consider the pattern \[\begin{aligned}L_1&:4^2-1^2=15\\L_2&:5^2-2^2=21\\L_3&:6^2-3^2=27\\L_4&:7^2-4^2=33\\&\ \vdots\\L_n&:\ldots\end{aligned}\]

1. Write down \(L_n\) of the pattern.[1]
2. Explain, with working, whether 3336 is a term of the sequence 15, 21, 27, 33, …[2]
3. Find the exact value of \(L_1+L_4+L_7+L_{10}+L_{13}+\cdots+L_{97}+L_{100}\).[2]