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# Solve the equation

Question:

Let $A$ be the sum of the first 20 terms and B be the sum of the first 40 terms of the series $1^{2}+2 \cdot 2^{2}+3^{2}+2 \cdot 4^{2}+5^{2}+2 \cdot 6^{2}+\ldots \ldots \ldots$ If $\mathrm{B}-2 \mathrm{~A}=100 \lambda$, then $\lambda$ is equal to :

1. 248

2. 464

3. 496

4. 232

Correct Option: 1

Solution: