if the first term of a geometric sequence is 0.9 and its ratio is 0.2, what is the sum of the first five terms?

Question

if the first term of a geometric sequence is 0.9 and its ratio is 0.2, what is the sum of the first five terms?

Answer 1

a1 = .9

a2 = .9(.2) = .18

a3 = .18(.2)= .9(.2^2)= .9(.04) = .036

a4 = .036(.2) = .9(.2^3)=.9(.008)=0072

a5 = .00072(.2) = .9(.2^4) =.9(.0016) = .00144

a1+a2+a3+a4+a5= 1.116+.0072=1.1232+.00144 = 1.1248

sum of 1st five terms = 1.1248

formula for sum of a geometric series = Sn = .a1(1-r^n)/(1-r)

for 5th term, n=5,r=.2, a1=.9

S5 = .9(1-.2^5)/(1-.2) = (.9/.8)(1-.00032)=(9/8)(.99968)= 1.1248