A balloon rises 250 feet in first minute and then for each succeeding minute rises 70% as much as it did in the previous minute. How high will it be after 8 minutes

785 ft

Step-by-step explanation:

The increases in height can be modeled by a geometric series with first term 250 and common ratio 0.7. The sum of n terms of such a series is given by ...

Sn = 250 (1 - 0.7^n) / (1 - 0.7)

Then the 8th term, the height after 8 minutes, will be ...

S8 = 250 (1 -.057648) / (0.3) ≈ 785.3 ft

After 8 minutes, the balloon will be about 785 feet high.

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If it continues like that, its ultimate height will be about 833.3 feet.