Question

In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers

The number of bacteria in a certain food item after each second, when they double in every second.

Answer 1

Let the number of bacteria in a certain food = x

Since, they double in every second.

∴ `x, 2x, 2(2x), 2(2 * 2 * x),...`

i.e., `x, 2x, 4x, 8x, ...`

Now, let `t_1 = x, t_2 = 2x , t_3 - 4x` and `t_4 = 8x`

`t_2 - t_1 = 2x - x = x`

`t_3 - t_2 = 4x - 2x = 2x`

`t_4 - t_3 = 8x - 4x = 4x`

Since, the difference between each successive term is not same

So, the list does form an AP