Let a_n be the n^th term of a G.P. of positive terms. If Σ_n =1^100 a_2 n +1 =200 and Σ_n=1^100 a_2 n=100, then Σ_n=1^200 a_n is equal to:

Let $\displaystyle \mathbf{a}_{\mathbf{n}}$ be the $\displaystyle \mathbf{n}^{\text {th }}$ term of a G.P. of positive terms. If $\displaystyle \sum_{\mathrm{n}=1}^{100} \mathrm{a}_{2 \mathrm{n}+1}=200$ and $\displaystyle \sum_{n=1}^{100} a_{2 n}=100$, then $\displaystyle \sum_{n=1}^{200} a_n$ is equal to :