Question Number 199863 by Karanji last updated on 10/Nov/23
$$−\mathrm{5}+\left(−\mathrm{8}\right)+\left(−\mathrm{11}\right)+...+\left(−\mathrm{230}\right) \\ $$
Answered by som(math1967) last updated on 10/Nov/23
$$\:{c}.{d}=\left(−\mathrm{8}\right)−\left(−\mathrm{5}\right)=−\mathrm{3} \\ $$$$−\mathrm{230}=−\mathrm{5}\:+\left({n}−\mathrm{1}\right)×−\mathrm{3} \\ $$$$\Rightarrow\left({n}−\mathrm{1}\right)=\mathrm{75} \\ $$$$\Rightarrow{n}=\mathrm{76} \\ $$$${S}_{\mathrm{76}} =\frac{\mathrm{76}}{\mathrm{2}}\left\{−\mathrm{10}+\mathrm{75}×\left(−\mathrm{3}\right)\right\} \\ $$$$=\mathrm{38}×\left(−\mathrm{235}\right)=−\mathrm{8930} \\ $$
Commented by Karanji last updated on 10/Nov/23
$${sirthankyou} \\ $$
Commented by Karanji last updated on 10/Nov/23
$${happy}\:{diwali}\:{sir} \\ $$