Question

A type of organism's cells split every minute. If the organism has 4 cells when the cells begin to split, how many cells will the organism have after 6 minutes?

Answer 1

Answer:

The total of cells will the organism have after 6 minutes is 252

Step-by-step 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