Mathematics - Sequence & Series Question with Solution | TestHub

Because 1/a,1/b,1/c are in A.P., $(\mathrm{a}+\mathrm{b}+\mathrm{c})/\mathrm{a},(\mathrm{a}+\mathrm{b}+\mathrm{c})/\mathrm{b},(\mathrm{a}+\mathrm{b}+\mathrm{c})/\mathrm{c}$ are too; subtracting 1 or 2 proves D and A when defined. Also $\mathrm{b}(\mathrm{a}+\mathrm{c})=2\mathrm{ac}$, which simplifies B and gives $(\mathrm{a}-\mathrm{b}/2)(\mathrm{c}-\mathrm{b}/2)=(b/2{)}^2$, proving C.