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Question Number 93220 by I want to learn more last updated on 11/May/20

Please in an arithmetic mean a, A_1 , A_2 , A_3 , ... , A_n , b where A_1 , A_2 , A_3 , ... , A_n are nth arithmetic mean why is b = (n + 2)th term: like T_(n + 2) Please

$$\mathrm{Please}\:\mathrm{in}\:\mathrm{an}\:\mathrm{arithmetic}\:\mathrm{mean} \\ $$$$\:\:\:\:\:\:\:\mathrm{a},\:\:\mathrm{A}_{\mathrm{1}} ,\:\mathrm{A}_{\mathrm{2}} ,\:\mathrm{A}_{\mathrm{3}} ,\:...\:,\:\mathrm{A}_{\mathrm{n}} ,\:\mathrm{b} \\ $$$$\mathrm{where}\:\:\:\mathrm{A}_{\mathrm{1}} ,\:\mathrm{A}_{\mathrm{2}} ,\:\mathrm{A}_{\mathrm{3}} ,\:...\:,\:\mathrm{A}_{\mathrm{n}} \:\:\mathrm{are}\:\mathrm{nth}\:\mathrm{arithmetic}\:\mathrm{mean} \\ $$$$\mathrm{why}\:\mathrm{is}\:\:\mathrm{b}\:\:=\:\:\left(\mathrm{n}\:\:+\:\:\mathrm{2}\right)\mathrm{th}\:\:\mathrm{term}:\:\:\mathrm{like}\:\:\mathrm{T}_{\mathrm{n}\:\:+\:\:\mathrm{2}} \\ $$$$\mathrm{Please} \\ $$

Commented by Rasheed.Sindhi last updated on 12/May/20

determinant ((T_1 ,T_2 ,T_3 ,(...),T_n ,T_(n+1) ,T_(n+2) ),(a,A_1 ,A_2 ,(...),A_(n−1) ,A_n ,b))

$$\begin{vmatrix}{{T}_{\mathrm{1}} }&{{T}_{\mathrm{2}} }&{{T}_{\mathrm{3}} }&{...}&{{T}_{{n}} }&{{T}_{{n}+\mathrm{1}} }&{{T}_{{n}+\mathrm{2}} }\\{{a}}&{{A}_{\mathrm{1}} }&{{A}_{\mathrm{2}} }&{...}&{{A}_{{n}−\mathrm{1}} }&{{A}_{{n}} }&{{b}}\end{vmatrix} \\ $$

Commented by Rasheed.Sindhi last updated on 11/May/20

Account of terms in the AP number of AMs n number of first terms 1 number of last terms 1 _(−) Total terms n+2 Hence last term b=(n+2)th term

$$\:\:{Account}\:{of}\:{terms}\:{in}\:{the}\:{AP} \\ $$$${number}\:{of}\:{AMs}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{n} \\ $$$${number}\:{of}\:{first}\:{terms}\:\:\:\mathrm{1} \\ $$$$\underset{−} {{number}\:{of}\:{last}\:{terms}\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:}\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{Total}\:{terms}\:\:\:\:\:\:\:\:\:\:\:{n}+\mathrm{2} \\ $$$${Hence}\:{last}\:{term}\:\:{b}=\left({n}+\mathrm{2}\right){th}\:{term} \\ $$$$ \\ $$

Commented by I want to learn more last updated on 11/May/20

I appreciate sir.

$$\mathrm{I}\:\mathrm{appreciate}\:\mathrm{sir}. \\ $$

Commented by I want to learn more last updated on 11/May/20

Sir please show me how the term goes on: like T_1 + T_2 + ... + T_(n − 1) + T_n + ... + T_(n + 1) + T_(n + 2) Am i right

$$\mathrm{Sir}\:\mathrm{please}\:\mathrm{show}\:\mathrm{me}\:\mathrm{how}\:\mathrm{the}\:\mathrm{term}\:\mathrm{goes}\:\mathrm{on}: \\ $$$$\mathrm{like}\:\:\:\:\:\mathrm{T}_{\mathrm{1}} \:+\:\mathrm{T}_{\mathrm{2}} \:+\:...\:+\:\mathrm{T}_{\mathrm{n}\:−\:\mathrm{1}} \:+\:\mathrm{T}_{\mathrm{n}} \:+\:...\:+\:\mathrm{T}_{\mathrm{n}\:+\:\mathrm{1}} \:+\:\mathrm{T}_{\mathrm{n}\:+\:\mathrm{2}} \\ $$$$\mathrm{Am}\:\mathrm{i}\:\mathrm{right} \\ $$

Commented by I want to learn more last updated on 12/May/20

I understand sir. I appreciate

$$\mathrm{I}\:\mathrm{understand}\:\mathrm{sir}.\:\mathrm{I}\:\mathrm{appreciate} \\ $$

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