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Question Number 59336 by Tawa1 last updated on 08/May/19
Find the nth term of the AP:     2,    − (2/5) ,     − (2/(11)) , ...
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{AP}:\:\:\:\:\:\mathrm{2},\:\:\:\:−\:\frac{\mathrm{2}}{\mathrm{5}}\:,\:\:\:\:\:−\:\frac{\mathrm{2}}{\mathrm{11}}\:,\:… \\ $$
Answered by Forkum Michael Choungong last updated on 08/May/19
d= t_2 −t_1 =t_3 −t_2   ⇒ d= −((2/5)+2)=−(2/(11))+(2/5)       d= −((12)/5)≠((12)/(55))  not an AP
$${d}=\:{t}_{\mathrm{2}} −{t}_{\mathrm{1}} ={t}_{\mathrm{3}} −{t}_{\mathrm{2}} \\ $$$$\Rightarrow\:{d}=\:−\left(\frac{\mathrm{2}}{\mathrm{5}}+\mathrm{2}\right)=−\frac{\mathrm{2}}{\mathrm{11}}+\frac{\mathrm{2}}{\mathrm{5}} \\ $$$$\:\:\:\:\:{d}=\:−\frac{\mathrm{12}}{\mathrm{5}}\neq\frac{\mathrm{12}}{\mathrm{55}} \\ $$$${not}\:{an}\:{AP} \\ $$

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