Geometric Sequences

Question

A building is being constructed so that the 1st floor is 194131. square feet, the 2nd floor is 155305. square feet, the 3rd floor is 124244. square feet, and so on. The top floor is 916.758 square feet. How many floors does the building have?

 

How would I solve this?

Answer 1

r = 155,305/194,131 = .8

a_n = a₁(r^n-1)

916.758 = 194,131(.8^n-1)

.0047224 = .8^n-1

log_.8(.0047224) = n-1

(log.0047224)/(log .8) = n - 1

23.9999 = n - 1

25 floors = n