A car dealership sold one car in its first month of business. The number of cars it sold doubled each month.
What was the total number of cars the dealership sold during the first 12 months?
You can use exponential growth for this one:
2^N - 1, where N = Number of months
2^12 - 1
4,096 - 1
=4,095 - total number of cars sold in 12 months!!. Quite a dealership!!
You can also use GS to sum them up, where:
First term =1
Common ratio = 2
Number of terms = 12
You should get the same answer =4,095 cars.
In this case, you would do \(2^0+2^1+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9+2^10+2^11+ = 4095\). Since it doubles, it makes sense to use 2 as a base. Since it starts with one car, you start with a value that equals 1 (20) and continues all the way to 12 months later (211 ). You add all these up since you're asking for the total amt of cars spent in the first year.