Progressions!!!!?

Question

In a certain colony of bacteria, each bascillus divides into 2 every hour. If at the end of the first hour there are 2, how many will there be after 24 hours?

What kind of progression is applicable in this problem?

Answer 1

to solve this problem, you have to use Geometric Progression (G.P.)...

...as you will analyze the problem, it starts with 2 and doubles every hour...G.P. is a sequence of numbers wherein every term after the first is obtained by multiplying the term immediately preceeding by a fixed number, called the "common ratio"...what you need is the total number after 24 hours...

let's say:
a1 = 1st term
an = nth term
n = no. of terms
r = common ratio

formula for G.P.: an=a1r^(n-1)
substitute:
a24= 2(2)^(24-1)
a24= 2 (2)^23
therefore, a24= 16.777216x10E6

Answer 2

At the end of t=1 hour there are 2. At the end of t=2 hours there are 4. At the end of t=3 hours there are 8. And so on and so forth. The progression is 2^t. At the end of 24 hours there should be 2^24 = 16,777,216.

Answer 3

Geometric progression should be applied .
here a = 2 ,r = 2,n=24
so, tn = ar^(n-1) = 2*2^23 = 2^24 =(4096)^2 = 16777216

Answer 4

This doubles every hour. It is a geometric progression.

2 after 1 hour
T[1] = 2
T[2] = 4

T[n] = 2T[n-1] = 2^n
T[24] = 2^24 = 16,777,216

Answer 5

geometric progression P=a*q^n-1

first hour N(1)= 2*2^(1-1) =2^0=1
second hour N(2) = 2*2^(2-1) = 2*2=4

24 hour N(24) =2*2^(24-1) = 2*2^23

the sum is 2^24-1