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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.
Solution
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.
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