The sum of the first n terms of sequence 85 +85(.9) +85(.9)² + ... would be 348.08.
What is the sum of terms of a geometric sequence?
Let's suppose its initial term is a , multiplication factor is r and let it has total n terms,
then, its sum is given as:
[tex]S_n = \dfra[/tex][tex]\dfrac{a(r^n-1)}{r-1}[/tex]
(sum till nth term)
Given geometric sequence;
85 +85(.9) +85(.9)² + ...
a = 85
r = 0.9
its sum is given as:
[tex]S_n = \dfra[/tex][tex]\dfrac{a(r^n-1)}{r-1}[/tex]
[tex]S_n = \dfrac{85(0.9^5-1)}{0.9-1}\\\\S_n = \dfrac{85(0.5904-1)}{-0.1}\\\\\\S_n = \dfrac{85(-0.4095)}{-0.1}\\\\S_n = 348.08[/tex]
Thus,
The sum of the first n terms of sequence 85 +85(.9) +85(.9)² + ... would be 348.08.
Learn more about geometric sequence here:
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