Question Number 59336 by Tawa1 last updated on 08/May/19
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{AP}:\:\:\:\:\:\mathrm{2},\:\:\:\:−\:\frac{\mathrm{2}}{\mathrm{5}}\:,\:\:\:\:\:−\:\frac{\mathrm{2}}{\mathrm{11}}\:,\:… \\ $$
Answered by Forkum Michael Choungong last updated on 08/May/19
$${d}=\:{t}_{\mathrm{2}} −{t}_{\mathrm{1}} ={t}_{\mathrm{3}} −{t}_{\mathrm{2}} \\ $$$$\Rightarrow\:{d}=\:−\left(\frac{\mathrm{2}}{\mathrm{5}}+\mathrm{2}\right)=−\frac{\mathrm{2}}{\mathrm{11}}+\frac{\mathrm{2}}{\mathrm{5}} \\ $$$$\:\:\:\:\:{d}=\:−\frac{\mathrm{12}}{\mathrm{5}}\neq\frac{\mathrm{12}}{\mathrm{55}} \\ $$$${not}\:{an}\:{AP} \\ $$