Question Number 93220 by I want to learn more last updated on 11/May/20
$$\mathrm{Please}\:\mathrm{in}\:\mathrm{an}\:\mathrm{arithmetic}\:\mathrm{mean} \\ $$$$\:\:\:\:\:\:\:\mathrm{a},\:\:\mathrm{A}_{\mathrm{1}} ,\:\mathrm{A}_{\mathrm{2}} ,\:\mathrm{A}_{\mathrm{3}} ,\:…\:,\:\mathrm{A}_{\mathrm{n}} ,\:\mathrm{b} \\ $$$$\mathrm{where}\:\:\:\mathrm{A}_{\mathrm{1}} ,\:\mathrm{A}_{\mathrm{2}} ,\:\mathrm{A}_{\mathrm{3}} ,\:…\:,\:\mathrm{A}_{\mathrm{n}} \:\:\mathrm{are}\:\mathrm{nth}\:\mathrm{arithmetic}\:\mathrm{mean} \\ $$$$\mathrm{why}\:\mathrm{is}\:\:\mathrm{b}\:\:=\:\:\left(\mathrm{n}\:\:+\:\:\mathrm{2}\right)\mathrm{th}\:\:\mathrm{term}:\:\:\mathrm{like}\:\:\mathrm{T}_{\mathrm{n}\:\:+\:\:\mathrm{2}} \\ $$$$\mathrm{Please} \\ $$
Commented by Rasheed.Sindhi last updated on 12/May/20
$$\begin{vmatrix}{{T}_{\mathrm{1}} }&{{T}_{\mathrm{2}} }&{{T}_{\mathrm{3}} }&{…}&{{T}_{{n}} }&{{T}_{{n}+\mathrm{1}} }&{{T}_{{n}+\mathrm{2}} }\\{{a}}&{{A}_{\mathrm{1}} }&{{A}_{\mathrm{2}} }&{…}&{{A}_{{n}−\mathrm{1}} }&{{A}_{{n}} }&{{b}}\end{vmatrix} \\ $$
Commented by Rasheed.Sindhi last updated on 11/May/20
$$\:\:{Account}\:{of}\:{terms}\:{in}\:{the}\:{AP} \\ $$$${number}\:{of}\:{AMs}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{n} \\ $$$${number}\:{of}\:{first}\:{terms}\:\:\:\mathrm{1} \\ $$$$\underset{−} {{number}\:{of}\:{last}\:{terms}\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:}\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{Total}\:{terms}\:\:\:\:\:\:\:\:\:\:\:{n}+\mathrm{2} \\ $$$${Hence}\:{last}\:{term}\:\:{b}=\left({n}+\mathrm{2}\right){th}\:{term} \\ $$$$ \\ $$
Commented by I want to learn more last updated on 11/May/20
$$\mathrm{I}\:\mathrm{appreciate}\:\mathrm{sir}. \\ $$
Commented by I want to learn more last updated on 11/May/20
$$\mathrm{Sir}\:\mathrm{please}\:\mathrm{show}\:\mathrm{me}\:\mathrm{how}\:\mathrm{the}\:\mathrm{term}\:\mathrm{goes}\:\mathrm{on}: \\ $$$$\mathrm{like}\:\:\:\:\:\mathrm{T}_{\mathrm{1}} \:+\:\mathrm{T}_{\mathrm{2}} \:+\:…\:+\:\mathrm{T}_{\mathrm{n}\:−\:\mathrm{1}} \:+\:\mathrm{T}_{\mathrm{n}} \:+\:…\:+\:\mathrm{T}_{\mathrm{n}\:+\:\mathrm{1}} \:+\:\mathrm{T}_{\mathrm{n}\:+\:\mathrm{2}} \\ $$$$\mathrm{Am}\:\mathrm{i}\:\mathrm{right} \\ $$
Commented by I want to learn more last updated on 12/May/20
$$\mathrm{I}\:\mathrm{understand}\:\mathrm{sir}.\:\mathrm{I}\:\mathrm{appreciate} \\ $$