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.
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
Concept: Arithmetic Progression
Is there an error in this question or solution?