viviananaiah18 viviananaiah18
  • 23-04-2019
  • Mathematics
contestada

What is the sum of an infinite geometric series if a1 = 144 and r = 1⁄4?

A.288
B. 576
C. 252
D. 192

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jimrgrant1 jimrgrant1
  • 23-04-2019

Answer:

D

Step-by-step explanation:

The sum to infinity of a geometric sequence is

sum to infinity = [tex]\frac{a_{1} }{1-r}[/tex]

here [tex]a_{1}[/tex] = 144 and r = [tex]\frac{1}{4}[/tex], hence

sum = [tex]\frac{144}{1-\frac{1}{4} }[/tex]

      = [tex]\frac{144}{\frac{3}{4} }[/tex]

      = [tex]\frac{144(4)}{3}[/tex] = 192 → D

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