Question

what is the sum of an 8-term geometric series if the first term is -11, the last term is 180,224 and the common ratio is -4?

Answer 1

$a_1=-11;\ r=-4;\ a_8=180,224;\ S_8=?\\\\S_n=\dfrac{a_1(1-r^n)}{1-r}\\\\S_8=\dfrac{-11[1-(-4)^8]}{1-(-4)}=\dfrac{-11(1-65,536)}{1+4}=\dfrac{-11(-65,535)}{5}\\\\=-11\cdot(-13,107)=144,177$