To the nearest tenth, what is the sum of the infinite geometric series that begins with 10 + 2 + 2/5 + 2/25?

To determine the sum of the infinite geometric series starting with the terms 10, 2, 2/5, and 2/25, we first need to identify the first term and the common ratio of the series.

The first term, often represented as (a), is clearly 10. After that, the second term is 2. To find the common ratio (r), we can take the second term (2) and divide it by the first term (10):

[

r = \frac{2}{10} = 0.2

]

To ensure this common ratio holds for the subsequent terms, we can verify that it is consistent by taking the third term (2/5) and dividing it by the second term (2):

[

r = \frac{2/5}{2} = \frac{1}{5} = 0.2

]

Lastly, checking the next term (2/25) divided by the previous term (2/5) also confirms:

[

r = \frac{2/25}{2/5} = \frac{2/25 \times 5/2} = \frac{1}{5} =