Answer:
Initially, there were 50 memes.
Step-by-step explanation:
It is given that the number doubles daily.
Let the initial number = a
On 2nd day, the number = 2a
On 3rd day, the number = 2 [tex]\times[/tex] 2a
On 4th day, the number = 2 [tex]\times[/tex] 2 [tex]\times[/tex] 2a
and so on..
If we look closely, it is a Geometric Progression with
First term = a and
The common ratio, r = 2
Also, it is given that, 12th term:
[tex]a_{12}=102400[/tex]
nth term of a GP is given as:
[tex]a_n=ar^{n-1}[/tex]
So,
[tex]a_{12}=a \times r^{12-1}\\\Rightarrow 102400=a \times 2^{11}\\\Rightarrow a=\dfrac{102400}{2^{11}}\\\Rightarrow a=\dfrac{102400}{2048}\\\Rightarrow a = 50[/tex]
Hence, the answer is, the initial number is 50.
