Let a_1, a_2, …, a_10 be an AP with common difference -3 and b_1, b_2, …, b_10 be a GP with common ratio 2. Let c_k = a_k + b_k, k =1,2, …, 10. If…

Let $\displaystyle \mathrm{a}_1, \mathrm{a}_2, \ldots, \mathrm{a}_{10}$ be an AP with common difference -$\displaystyle 3$ and $\displaystyle \mathrm{b}_1, \mathrm{~b}_2, \ldots, \mathrm{~b}_{10}$ be a GP with common ratio 2. Let $\displaystyle \mathrm{c}_{\mathrm{k}}=\mathrm{a}_{\mathrm{k}}+\mathrm{b}_{\mathrm{k}}, \mathrm{k}=1,2, \ldots, 10$. If $\displaystyle \mathrm{c}_2=12$ and $\displaystyle \mathrm{c}_3=13$, then $\displaystyle \sum_{\mathrm{k}=1}^{10} \mathrm{c}_{\mathrm{k}}$ is equal to \_\_\_\_.