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 ______.
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 ______.
Solution
The sum of an infinite geometric sequence can be found using the formula S = a / (1 - r), where 'a' is the first term and 'r' is the common ratio.
Step 1: Identify the first term (a) and the common ratio (r). The first term (a) is 90. The common ratio (r) can be found by dividing the second term by the first term, or the third term by the second term. So, r = 22.5 / 90 = 0.25.
Step 2: Substitute the values of 'a' and 'r' into the formula. S = 90 / (1 - 0.25) = 90 / 0.75 = 120.
Therefore, the sum of all the terms in the sequence is 120.
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