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 t₁ = x, t₂ = 2x, t₃ – 4x and t₄ = 8x

t₂ – t₁ = 2x – x = x

t₃ – t₂ = 4x – 2x = 2x

t₄ – t₃ = 8x – 4x = 4x

Since, the difference between each successive term is not same.

So, the list does form an AP.