Find the sum of geometric series described as: a1=10, n=20, r=1.5

Question

The Landbury Museum has been investing in paintings for many years. 20 years ago, the museum purchased a painting by on of the French Impressionist painters for $180,000. If they painting has appreciated at a rate of 14% per year, find the value of the painting after 10,15 and 20 years.

Answer 1

The painting is worth 180000(1.14)^n where n=10, 15 or 20: $667,300, $M1.285, $M2.474, where $M is a million dollars.

The sum of the GP is 10(1.5^20-1)/0.5=66,485.13.