Mathematics - Sequence & Series Question with Solution | TestHub

Put $(\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d})=\mathrm{a}\left(1,\mathrm{r},r^2,r^3\right)$. The A.P. second-difference equations yield $\mathrm{a}(r-1{)}^2=-3$ and $\mathrm{ar}(r-1{)}^2=-6$. Thus $\mathrm{r}=2,\mathrm{a}=-3$, and the sum is -45, divisible by 3 and 5.