For |α| ≥ 1, let 5^4-2 α, 63,5^2 α-1 be in A.P. with the common difference d. Let S_n denote the sum of the first n terms of an A.P., whose first…

For $\displaystyle |\alpha| \geq 1$, let $\displaystyle 5^{4-2 \alpha}, 63,5^{2 \alpha-1}$ be in A.P. with the common difference d. Let $\displaystyle \mathrm{S}_{\mathrm{n}}$ denote the sum of the first n terms of an A.P., whose first term is $\displaystyle \alpha^2$ and the common difference is d . If $\displaystyle \mathrm{S}_{30}-\mathrm{S}_{15}=30 \mathrm{k}$, then k is equal to