The equation that represents the partial sum of the geometric series is 125, 25, 5, 1
Given the partial sum of a geometric sequence expressed as:
[tex]\sum\left { n=4 \atop {n=1}} \right. 125(\frac{1}{5} )^{n-1}[/tex]
If n = 1, the
a(1) = [tex]125(\frac{1}{5} )^{1-1}\\[/tex]
a(1) = [tex]125(\frac{1}{5} )^{0}\\[/tex]
a(1) = 125
If n = 2
a(2) = [tex]125(\frac{1}{5} )^{2-1}\\[/tex]
a(2) = [tex]125(\frac{1}{5} )^{1}\\[/tex]
a(2) = 25
If n = 3
a(3)= [tex]125(\frac{1}{5} )^{3-1}\\[/tex]
a(3) = [tex]125(\frac{1}{5} )^{2}\\[/tex]
a(3) = 5
If n = 4
a(4)= [tex]125(\frac{1}{5} )^{4-1}\\[/tex]
a(4) = [tex]125(\frac{1}{5} )^{3}\\[/tex]
a(4) = 1
Hence the equation that represents the partial sum of the geometric series is 125, 25, 5, 1
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