After release at ground level, a balloon rises 100 feet in 30 seconds. During each succeeding 30 seconds, it rises 9/10

as far as it did in the preceding 30 seconds. What is its maximum altitude above ground level?

I know its supposed to be 1000 feet, but I just don't know how to get there. Any help would be great! Thanks so much:)

To find the maximum altitude of the balloon above ground level, we need to determine the total distance it travels during its ascent.

In the first 30 seconds, the balloon rises 100 feet.

In the next 30-second interval, the balloon rises 9/10 * 100 = 90 feet.

In the next 30-second interval, the balloon rises 9/10 * 90 = 81 feet.

This pattern will continue until the balloon stops rising altogether.

To find the sum of this series, we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r),

where S is the sum of the series, a is the first term, and r is the common ratio.

a = 100 (the first term)
r = 9/10 (the common ratio)

S = 100 / (1 - 9/10)
S = 100 / (1/10)
S = 1000

So, the sum of the series is 1000 feet.

Therefore, the maximum altitude of the balloon above ground level is 1000 feet.