Question Number 141197 by paulpadas last updated on 16/May/21
$${Write}\:{the}\:{next}\:{three}\:{terms}\:\mathrm{1},\:\frac{\mathrm{3}}{\mathrm{7}},\:\frac{\mathrm{8}}{\mathrm{3}},\:\_\_\_,\:\_\_\_,\:\_\_\_,\:... \\ $$
Answered by MJS_new last updated on 16/May/21
$$\mathrm{zillions}\:\mathrm{of}\:\mathrm{possible}\:\mathrm{answers}. \\ $$$$\mathrm{I}\:\mathrm{like}\:\mathrm{this}\:\mathrm{one} \\ $$$${a}_{{n}} =−\frac{\mathrm{3}}{\mathrm{10}}−\frac{\mathrm{38}{n}−\mathrm{25}}{\mathrm{10}\left(\mathrm{5}{n}^{\mathrm{2}} −\mathrm{21}{n}+\mathrm{15}\right)} \\ $$$${a}_{{n}} =\langle\mathrm{1},\:\frac{\mathrm{3}}{\mathrm{7}},\:\frac{\mathrm{8}}{\mathrm{3}},\:−\frac{\mathrm{16}}{\mathrm{11}},\:−\frac{\mathrm{27}}{\mathrm{35}},\:...\rangle \\ $$
Commented by Ar Brandon last updated on 16/May/21
Hi ! Nice week-end Sir ! ��
Commented by MJS_new last updated on 16/May/21
for you too!
Commented by Ar Brandon last updated on 16/May/21
$$\:\mathrm{I}\:\mathrm{finally}\:\mathrm{got}\:\mathrm{a}\:\mathrm{chance}\:\mathrm{to}\:\mathrm{apply}\:\mathrm{the}\:\mathrm{method}\:\mathrm{you}\:\mathrm{taught} \\ $$$$\mathrm{me}\:\mathrm{last}\:\mathrm{year}.\:\mathrm{First}\:\mathrm{on}\:\mathrm{Q140789}\:\mathrm{and}\:\mathrm{then}\:\mathrm{Q140976} \\ $$$$\mathrm{Did}\:\mathrm{you}\:\mathrm{see}\:\mathrm{it},\:\mathrm{Sir}\:? \\ $$
Commented by Ar Brandon last updated on 16/May/21
$$\mathrm{Q140976} \\ $$
Commented by MJS_new last updated on 16/May/21
$$\mathrm{yes}!\:\mathrm{I}'\mathrm{m}\:\mathrm{honoured}...\: \\ $$
Commented by Ar Brandon last updated on 16/May/21
$$\mathrm{Vielen}\:\mathrm{dank}\:! \\ $$