Question

What is the sum of the geometric sequence 1,-6,36... if there are 6 terms

Answer 1

`a_1=1;\ a_2=-6;\ a_3=36;\ ...\\\\r=a_2:a_1\to r=-6:1=-6\\\\S_n=(a_1(1-r^n))/(1-r)\\\\a_1=1;\ r=-6;\ n=6\\\\subtitute\\\\S_6=(1(1-(-6)^6))/(1-(-6))=(1-46656)/(1+6)=(46655)/(7)=6665`