Question Number 29645 by gyugfeet last updated on 11/Feb/18 $${if}\:{the}\:{sum}\:{of}\:{first}\:\mathrm{5}\:{terms}\:{of}\:\:{a}\:{G}.{P}.\:{is}\:\mathrm{155},\:{sum}\:{of}\:{last}\:\mathrm{5}\:{terms}\:{is}\:\mathrm{39680},{first}\:{term}\:{is}\:\mathrm{5}\:{and}\:{last}\:{term}\:\:{is}\:\mathrm{20480}.\:{find}\:{the}\:{number}\:{of}\:{terms}\:{of}\:{the}\:{sequence}. \\ $$ Answered by Rasheed.Sindhi last updated on 11/Feb/18 $$\mathrm{Let}\:\mathrm{the}\:\mathrm{common}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{GP}\:\mathrm{is}\:\mathrm{r} \\ $$$$\mathrm{Sum}\:\mathrm{of}\:\mathrm{first}\:\mathrm{five}\:\mathrm{terms}: \\ $$$$\mathrm{5}+\mathrm{5r}+\mathrm{5r}^{\mathrm{2}} +\mathrm{5r}^{\mathrm{3}}…
Question Number 29643 by gyugfeet last updated on 11/Feb/18 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 94925 by I want to learn more last updated on 21/May/20 Commented by mr W last updated on 22/May/20 $${AB}={AC}={BC}={Radius} \\ $$$$\Rightarrow\Delta{ABC}={equilateral} \\…
Question Number 94921 by peter frank last updated on 21/May/20 Answered by Kunal12588 last updated on 22/May/20 Commented by Kunal12588 last updated on 22/May/20 Commented…
Question Number 160350 by Lekhraj last updated on 28/Nov/21 Answered by Rasheed.Sindhi last updated on 28/Nov/21 $$\mathrm{2001}\:\:\:\:\:{Let}\:{ages}\:{were}\:{x}\:\&\:\mathrm{11}{x} \\ $$$$\mathrm{2018}\:\:\:\:\:\:{x}+\mathrm{17}:\mathrm{11}{x}+\mathrm{17}=\mathrm{2}:\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{5}\left({x}+\mathrm{17}\right)=\mathrm{2}\left(\mathrm{11}{x}+\mathrm{17}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{5}{x}+\mathrm{85}=\mathrm{22}{x}+\mathrm{34} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{17}{x}=\mathrm{51}\Rightarrow{x}=\mathrm{3}…
Question Number 29169 by abdo imad last updated on 04/Feb/18 $${factorize}\:{inside}\:{R}\left[{x}\right]\:{the}\:{polynomial} \\ $$$${p}\left({x}\right)=\:{x}^{\mathrm{8}} −\mathrm{1}. \\ $$ Commented by abdo imad last updated on 06/Feb/18 $${p}\left({x}\right)=\left({x}^{\mathrm{4}}…
Question Number 29163 by abdo imad last updated on 04/Feb/18 $${let}\:{give}\:\left({n},{p}\right)\:{from}\:{N}^{\mathrm{2}} \:{and}\:\mathrm{1}\leqslant{p}\leqslant{n}\:{prove}\:{that}\: \\ $$$$\sum_{{k}=\mathrm{0}} ^{{p}} \:{C}_{{n}} ^{{k}} \:{C}_{{n}−{k}} ^{{p}−{k}} ==\mathrm{2}^{{p}} \:\:{C}_{{n}} ^{{p}} . \\ $$$$…
Question Number 94602 by peter frank last updated on 19/May/20 Answered by mr W last updated on 21/May/20 Commented by mr W last updated on…
Question Number 94573 by Ar Brandon last updated on 19/May/20 $$\mathrm{Given}\:\mathrm{a},\:\mathrm{b},\:\mathrm{and}\:\mathrm{c},\:\mathrm{3}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{which}\:\mathrm{satisfy} \\ $$$$\mathrm{the}\:\mathrm{equation}\:\begin{cases}{\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{312}}\\{\mathrm{c}+\mathrm{a}=\mathrm{192}}\end{cases} \\ $$$$\mathrm{Find}\:\mathrm{these}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that}\:\mathrm{they}\:\mathrm{form} \\ $$$$\mathrm{3}\:\mathrm{consecutive}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{Geometric}\:\mathrm{Progression}. \\ $$ Commented by mr W last updated…
Question Number 29035 by abdo imad last updated on 03/Feb/18 $${let}\:{give}\:{a}\:{prime}\:{number}\:{p}>\mathrm{2}\:\:{and}\:{a}\:/{D}\left({a},{p}\right)=\mathrm{1}\:{and}\: \\ $$$$\left.{suppose}\:{that}\:{the}\:{equation}\:{x}^{\mathrm{2}} \equiv\:{a}\left[{p}\right]{have}\:{a}\:{solution}\mathrm{1}\right) \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\:\:{a}^{\frac{{p}−\mathrm{1}}{\mathrm{2}}} \:\:\:\equiv\:\mathrm{1}\:\left[{p}\right] \\ $$$$\left.\mathrm{2}\right){prove}\:{that}\:\:{x}^{\mathrm{2}} \equiv\:−\mathrm{1}\left[{p}\right]\:\Leftrightarrow\:\:\:{p}\equiv\:\mathrm{1}\:\left[\mathrm{4}\right] \\ $$ Terms of Service…