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Author: Tinku Tara

The-first-term-of-an-arithmetic-series-is-7-and-the-last-is-70-and-the-sum-is-385-find-the-number-of-terms-in-the-series-and-its-common-difference-

Question Number 192450 by Mastermind last updated on 18/May/23 $$\mathrm{The}\:\mathrm{first}\:\mathrm{term}\:\mathrm{of}\:\mathrm{an}\:\mathrm{arithmetic}\:\mathrm{series} \\ $$$$\mathrm{is}\:\mathrm{7}\:\mathrm{and}\:\mathrm{the}\:\mathrm{last}\:\mathrm{is}\:\mathrm{70}.\:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{is} \\ $$$$\mathrm{385}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{series}\:\mathrm{and}\:\mathrm{its}\:\mathrm{common}\:\mathrm{difference}. \\ $$ Answered by AST last updated on 18/May/23…

The-sum-of-three-numbers-in-arith-metic-progression-is-18-and-sum-of-square-is-206-find-the-numbers-

Question Number 192444 by Mastermind last updated on 18/May/23 $$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{three}\:\mathrm{numbers}\:\mathrm{in}\:\mathrm{arith}- \\ $$$$\mathrm{metic}\:\mathrm{progression}\:\mathrm{is}\:\mathrm{18}\:\mathrm{and}\:\mathrm{sum}\:\mathrm{of} \\ $$$$\mathrm{square}\:\mathrm{is}\:\mathrm{206}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{numbers} \\ $$ Commented by Tinku Tara last updated on 19/May/23 $$\mathrm{Automatic}\:\mathrm{tagging}\:\mathrm{may}\:\mathrm{sometime}…

Given-A-p-2-q-2-r-2-2-pq-2-pr-2-qr-2-B-q-2-pr-p-2-q-2-r-2-If-p-q-r-0-then-A-2-4B-

Question Number 192440 by cortano12 last updated on 18/May/23 $$\:\:\:\:\mathrm{Given}\:\begin{cases}{\mathrm{A}=\frac{\left(\mathrm{p}^{\mathrm{2}} +\mathrm{q}^{\mathrm{2}} +\mathrm{r}^{\mathrm{2}} \right)^{\mathrm{2}} }{\left(\mathrm{pq}\right)^{\mathrm{2}} +\left(\mathrm{pr}\right)^{\mathrm{2}} +\left(\mathrm{qr}\right)^{\mathrm{2}} }}\\{\mathrm{B}=\frac{\mathrm{q}^{\mathrm{2}} −\mathrm{pr}}{\mathrm{p}^{\mathrm{2}} +\mathrm{q}^{\mathrm{2}} +\mathrm{r}^{\mathrm{2}} }\:}\end{cases}\:\:\:\:\:\: \\ $$$$\:\mathrm{If}\:\mathrm{p}+\mathrm{q}+\mathrm{r}=\mathrm{0}\:\mathrm{then}\:\mathrm{A}^{\mathrm{2}} −\mathrm{4B}=? \\…