Question

what is the sum of the first five terms of a geometric series with a 1=20 and r=1/4 please help me!!!

Answer 1

`a_1=20;\ r=(1)/(4);\ n=5\\\\S_n=(a_1(1-r^n))/(1-r)\\\\S_5=(20\cdot\left[1-\left((1)/(4)\right)^5\right])/(1-(1)/(4))=(20\cdot\left(1-(1)/(1024)\right))/((3)/(4))`


`=(20\cdot(1023)/(1024))/((3)/(4))=(20460)/(1024)\cdot(4)/(3)=(6820)/(256)=(1705)/(64)=26(41)/(64)\\\\Answer:\boxed{S_5=26(41)/(64)}`