Question

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 ______.

Answer 1

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

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