janayplacencia9 janayplacencia9
  • 18-03-2019
  • Mathematics
contestada

What is the sum of an infinite geometric series if the first term is 156 and the common ratio is 2⁄3?

A. 260
B. 468
C. 208
D. 234

Respuesta :

gmany
gmany gmany
  • 20-03-2019

Answer:

B. 468

Step-by-step explanation:

We have

[tex]a_1=156,\ r=\dfrac{2}{3}[/tex]

If |r| < 1, then the formula of a sum of an infinite geometric sequence is:

[tex]S=\dfrac{a_1}{1-r}[/tex]

Substitute:

[tex]S=\dfrac{156}{1-\frac{2}{3}}=\dfrac{156}{\frac{1}{3}}=156\cdot\dfrac{3}{1}=468[/tex]

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