Question

-5+(-8)+(-11)+ .......(-230)​

Answer 1

$\large\sf\underline\red{GIVEN:-}$

$\large\tt\purple{a=-5}$

$\large\tt\purple{d=-8-(-5)=-3}$

$\small\tt\green{Let\:the\:nth\:term\:of\:the\:AP\:is\:-230}$

$\therefore$$\large\tt\orange{an=-230}$

$\longrightarrow$$\small\tt\red{a+(n-1)d=-230}$

$\longrightarrow$$\small\tt\red{-5+(n-1)(-2)=-230}$

$\longrightarrow$$\small\tt\red{(n-1)(-3)=-225}$

$\longrightarrow$$\small\tt\red{n-1=75}$

$\longrightarrow$$\small\tt\red{n=75}$

$\small\sf\green{The\:sum\:of\:n\:terms\:of\:an\:AP\:is\:given\:by}$

$\longrightarrow$$\large\sf\pink{Sn=\frac{n}{2}(a+l)}$

$\longrightarrow$$\large\sf\pink{S76=\frac{76}{2}(-5-230)}$

$\longrightarrow$$\large\sf\pink{S76=\frac{76}{2}(-235)}$

$\longrightarrow$$\large\sf\pink{S76=-38×235}$

$\longrightarrow$$\large\sf\pink{S76=-8930}$