Let \( \mathrm{S} \) be the sum of the first 9 terms of the series : \( \{x+k a\}+\left\{x^{2}+(k+2) a\right\}+\left\{x^…

Let \( \mathrm{S} \) be the sum of the first 9 terms of the series : \( \{x+k a\}+\left\{x^{2}+(k+2) a\right\}+\left\{x^{3}+(k+4) a\right\}+\left\{x^{4}+\right. \) \( (\mathrm{k}+6) \mathrm{a}\}+\ldots \) where \( \mathrm{a} \neq 0 \) and \( \mathrm{x} \neq 1 \). If \( S=\frac{x^{10}-x+45 a(x-1)}{x-1} \), then \( k \) is equal to

[JEE Main 2020, 2 Sep (Shift 2)]