Question

4) Before mandatory school closures, memes about how tough teaching is/how we

should appreciate teachers were limited. Since "Operation Home School" was forced

to begin, the numbers double daily. If there are 102,400 memes after 12 days, how

many were there originally?

Answer 1

Initially, there were 50 memes.

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
`*` 2a

On 4th day, the number = 2
`*` 2
`*` 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:

`a_(12)=102400`

nth term of a GP is given as:

`a_n=ar^(n-1)`

So,

`a_(12)=a * r^(12-1)\\\Rightarrow 102400=a * 2^(11)\\\Rightarrow a=(102400)/(2^(11))\\\Rightarrow a=(102400)/(2048)\\\Rightarrow a = 50`

Hence, the answer is, the initial number is 50.