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emmainna [20.7K]
2 years ago
10

If the first 3 terms of an infinite geometric sequence are 90, 22.5, and 5.625, then the sum of all the terms in the sequence is

______.
Mathematics
1 answer:
zhannawk [14.2K]2 years ago
3 0

The sum of all the terms in the sequence is 120

Step-by-step explanation:

The sum of the all terms in an infinite geometric sequence is

S_{infinite}=\frac{a}{1-r} , where

  • a is the first term
  • r is the common ratio between each two consecutive terms
  • r=\frac{a_{2}}{a_{1}} OR r=\frac{a_{3}}{a_{2}}

The sum of all terms in the infinite geometric sequence = S_{infinite}

∵ The first 3 terms of an infinite geometric sequence are 90, 22.5,

   and 5.625

∴ a = 90

∵ r=\frac{a_{2}}{a_{1}}

∴ r=\frac{22.5}{90}=0.25

∵ S_{infinite}=\frac{a}{1-r}

∴ S_{infinite}=\frac{90}{1-0.25}

∴ S_{infinite}=\frac{90}{0.75}

∴ S_{infinite}=120

The sum of all the terms in the sequence is 120

Learn more:

You can learn more about sequences in brainly.com/question/3280369

#LearnwithBrainly

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