Answer:
The total of cells will the organism have after 6 minutes is 252
Explanation:
* Lets consider this problem as a geometric series
- There is a constant ratio between each two consecutive numbers
Ex:
# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)
# 5000 , 1000 , 200 , 40 , …………………………(÷5)
* General term (nth term) of a Geometric series:
∵ U1 = a , U2 = ar , U3 = ar^2 , U4 = ar^3 , U5 = ar^4
∴ Un = ar^n-1
- Where r is the ratio between each two consecutive terms and
n is the position of the number in the series
* The sum of first n terms of a Geometric Progression is calculate from
Sn = a(1 - r^n)/1 - r
- In the problem the cell split every minute
- The organism has 4 cells when the cells begin to split
∴ a = 4
# 4 , 8 , 16 , 32 , .......
∴ r = 2
- The total of cells will the organism have after 6 minutes can
calculate from the rule of the sum
∴ S6 = 4(1 - 2^6)/1 - 2 = 4(1 - 64)/-1 = 4(-63)/-1 = 252 cells