$$\begin{aligned} & 1+3+5^2+7+9^2+\ldots \text { upto } 40 \text { terms } \\ & \left(1^2+5^2+9^2+\ldots\right)+(3+7+11+\ldots) \\ & =\left(\sum_{k=1}^{20}(4 k-3)^2\right)+\frac{20}{2}[6+(20-1) 4] \\ & =16 \sum_{k=1}^{20} k^2-24 \sum_{k=1}^{20} k+9 \times 20+10[82] \\ & =16\left(\frac{20 \times 21 \times 41}{6}\right)-24\left(\frac{20 \times 21}{2}\right)+1000 \\ & =45920-5040+1000 \\ & =41880 \end{aligned}$$