Question Number 49487 by Tawa1 last updated on 07/Dec/18
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sequence}:\:\:\mathrm{5},\:\:\mathrm{5},\:\:\mathrm{35},\:\mathrm{65},\:\:\mathrm{275},\:... \\ $$$$ \\ $$$$\mathrm{Answer}:\:\:\:\:\:\mathrm{3}^{\boldsymbol{\mathrm{n}}} \:−\:\left(−\:\mathrm{2}\right)^{\boldsymbol{\mathrm{n}}} \:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{ple}}\mathrm{1ase}\:\mathrm{how} \\ $$
Commented by mr W last updated on 07/Dec/18
$${there}\:{is}\:{no}\:{unique}\:{solution}\:{for}\:{such} \\ $$$${questions}.\:{you}\:{can}\:{only}\:{check}\:{if}\:\mathrm{3}^{{n}} −\left(−\mathrm{2}\right)^{{n}} \\ $$$${is}\:{a}\:{solution},\:{but}\:{you}\:{can}\:{not}\:{say}\:{it}\:{is} \\ $$$${the}\:{only}\:{solution},\:{therefore}\:{you}\:{can} \\ $$$${not}\:{get}\:{it}. \\ $$$${in}\:{general},\:{if}\:{you}\:{know}\:{the}\:{first}\:\mathrm{5}\:\left({or}\:{any}\:{other}\right. \\ $$$$\left.{number}\right)\:{terms},\:{there}\:{are}\:{infinite} \\ $$$${possiblities}\:{what}\:{the}\:{following}\:{terms} \\ $$$${are},\:{you}\:{can}\:{give}\:{a}\:{formula}\:{for}\:{the} \\ $$$${nth}\:{term}\:{according}\:{to}\:{these}\:{known}\:{terms}, \\ $$$${but}\:{this}\:{formula}\:{is}\:{always}\:{only}\:{one} \\ $$$${of}\:{the}\:{infinite}\:{possibilities}.\:{somebody} \\ $$$${may}\:{give}\:{a}\:{different}\:{formula}\:{which} \\ $$$${also}\:{fulfills}\:{the}\:{first}\:{known}\:{terms}. \\ $$
Commented by Tawa1 last updated on 07/Dec/18
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$