Sequences and Series

Geometric Series

Sn = a1(1 - qⁿ)/(1 - q)

  • High school
  • about 3 min
  • 4 of 10 in the family
Not started
Cumulative sum2.001.000.500.25S1=2.00S2=3.00S3=3.50S4=3.75S5=3.88S6=3.94
a₁=2
q=0.50
n=6
Sn=a11−qn1−q=21−0.561−0.5=3.9375S_n = a_1\frac{1-q^n}{1-q} = 2\frac{1-0.5^{6}}{1-0.5} = 3.9375

The sum of a geometric sequence = the total colored bar width. Each term adds a smaller and smaller piece.