Question

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

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

Answer 1

Let the number of bacteria be x
Therefore

Case 1 ----> 1st second = x bacteria
Case 2 ----> 2nd second = 2x bacteria
Case 3 ----> 3rd second = 4x bacteria
Case 4 ----> 4th second = 8x bacteria


We got

x, 2x, 4x, 8x,..........

clearly a2 - a1 is not equal to a3 - a2
2x - x = x
8x - 4x = 4x

x is not equal to 4x

Therefore the following numbers are not in AP