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

a.) 300
b.) 118
c.) 360
d.) 120

Answer 1

The sum of all the terms in the infinite geometric sequence is 120.

Step-by-step explanation:

In an infinite geometric sequence, the common ratio between consecutive terms is the same. To find the common ratio, we can divide any term by the previous term. The common ratio for this sequence can be found by dividing 22.5 by 90, which gives us 0.25.

To find the sum of an infinite geometric sequence, we can use the formula S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio. Plugging in the values from the given sequence, we have S = 90 / (1 - 0.25) = 90 / 0.75 = 120.

Therefore, the sum of all the terms in the sequence is 120. So the correct option is d.) 120.