The sum of n terms of a geometric progression is [tex]S_n = 6(1 - 0.4^n)[/tex] .So, this progression defines the Sn rule.
What is the S rule?
The rule of S means that we calculate the rule that defines the sum of n in terms of the geometric progression.
Given that:
[tex]a_n = 9(0.4)^n[/tex]
We can write as
[tex]a_n = 9(0.4)^n \times 1\\\\ a_n = 9(0.4)^n\times \frac{0.4}{0.4} \\\\ a_n = 9(0.4)\times \frac{0.4^n}{0.4}[/tex]
Apply the law of indices
[tex]a_n = 9\times (0.4)\times {0.4^{n-1}}\\\\ a_n = 3.6\times {0.4^{n-1}}[/tex]
The n term of a geometric progression is
[tex]a_n = ar^{n-1}[/tex]
By comparing the above equation with the general form of geometric progression, we get
a = 3.6
r = 0.4
The sum of n terms of a geometric progression is:
[tex]S_n = \dfrac{a(r^n-1)}{r-1} \\\\S_n = \dfrac{3.6(0.4^n-1)}{0.4-1} \\\\S_n = 6(1 - 0.4^n)[/tex]
Learn more about the sum of geometric progression at:
brainly.com/question/22068689
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