Question

Workers are busy building a new skyscraper. As the building grows, the work

becomes more dangerous and difficult, so progress slows. During the first
month of construction, 50 vertical feet are built. Each month, the number of
additional feet added to the building decreases by 19%. How tall is the
building after 10 months?

Answer 1

• first term: 50
• number of terms: 10
• common ratio: 0.81
• series sum: 231.16

Explanation:

You want the sum of 10 terms of a geometric series that starts with 50 and has terms that decrease by 19% from the previous term.

Series sum

The first term is 50 feet, the amount of construction in the first month.

The number of terms is 10, the number of months construction proceeds.

The common ratio is 1 -19% = 81% = 0.81, the fraction each term is of the previous term.

The series sum is given by the formula ...

Sn = a1·(1 -r^n)/(1 -r)

Sn = 50·(1 -0.81^10)/(1 -0.81) ≈ 50·(0.878423/0.19) ≈ 231.16

The series sum is about 231.16 feet.

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