Let a_1, a_2, a_3, …. be in an A.P. such that Σ_k =1^12 a_2 k -1 =-72/5 a_1, a_1 ≠ 0. If Σ_k =1^n a_k =0, then n is:

Let $\displaystyle \mathrm{a}_1, \mathrm{a}_2, \mathrm{a}_3, \ldots . \mathrm{be}$ in an A.P. such that $\displaystyle \sum_{\mathrm{k}=1}^{12} \mathrm{a}_{2 \mathrm{k}-1}=-\frac{72}{5} \mathrm{a}_1, \mathrm{a}_1 \neq 0$. If $\displaystyle \sum_{\mathrm{k}=1}^{\mathrm{n}} \mathrm{a}_{\mathrm{k}}=0$, then n is: