Question Number 76428 by TawaTawa last updated on 27/Dec/19
Answered by john santu last updated on 27/Dec/19
$$\left(\mathrm{5}\right){ratio}\:=\:\frac{{a}_{\mathrm{2}} }{{a}_{\mathrm{1}} }.\:\rightarrow{a}_{\mathrm{2}} =\mathrm{10}.{a}_{\mathrm{1}} =\mathrm{10}. \\ $$$${now}\:{a}_{{n}\:} ={a}_{\mathrm{1}} ×{r}^{{n}−\mathrm{1}} =\mathrm{1}×\mathrm{10}^{{n}−\mathrm{1}} \\ $$
Commented by TawaTawa last updated on 27/Dec/19
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$
Answered by john santu last updated on 27/Dec/19
$${b}\:=\:{a}_{{n}\:} −\:{a}_{{n}−\mathrm{1}} =−\mathrm{4}. \\ $$$${so}\:{a}_{{n}\:} ={a}_{\mathrm{1}} +\left({n}−\mathrm{1}\right)×{b} \\ $$$$=\:−\mathrm{3}+\mathrm{4}−\mathrm{4}{n}\:=\mathrm{1}−\mathrm{4}{n} \\ $$