Math algebra 110

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 

Answer 1

The general formula for finding the sum of an infinite geometric series is a₁ / (1-r), where s is the sum, a₁ is the first term of the series, and r is the common ratio. 

r can be found by dividing any 2 consecutive numbers in the sequence. In our problem, we divide 22.5 by 90 or 5.625 by 22.5

Doing so we get r = 22.5/90 = 0.25 or 5.625/22.5 = 0.25

Thus, the sum of the infinite series is = a₁ / (1-r) = 90 / (1 - 0.25) = 90 / 0.75 = 120