Question

Find the sum of the geometric series.
30-6+1.20-…
The sum of the series is __

Answer 1

The sum of the geometric series 30 - 6 + 1.20 is found by using the sum formula for an infinite geometric series, resulting in a sum of 25.

Step-by-step explanation:

To find the sum of the geometric series 30 - 6 + 1.20, we first need to identify the common ratio. The common ratio (r) of a geometric series is found by dividing any term by the term preceding it. In this case:

• r = (-6) / 30 = -1/5
• r = 1.20 / (-6) = -1/5

Since the common ratio is consistent at -1/5, we can confirm it's a geometric series.

The sum of an infinite geometric series can be found using the formula S = a / (1 - r), where 'a' is the first term and 'r' is the common ratio, provided that the absolute value of 'r' is less than 1.

Applying the formula:

• a = 30
• r = -1/5

S = 30 / (1 - (-1/5))

S = 30 / (1 + 1/5)

S = 30 / (6/5)

So, S = 25. The sum of the series is 25.