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  • 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.

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.

Answers (1)

Answer.          [No]

Solution.        

Let number of bacteria = x

According to question:

They double in every second.

\\$ \therefore x, 2x, 2(2x), 2(2 \times 2x)$ \ldots $ $ \ldots $ $ \ldots $ $ \ldots $ $ \ldots $ \\ Here a\textsubscript{1 }= x , a\textsubscript{2 }=2x, a\textsubscript{3 }=4x, a\textsubscript{4}=8x\\ x, 2x, 4x, 8x$ \ldots $ ..$ \ldots $ ..\\ a\textsubscript{2} - a\textsubscript{1} = 2x - x = x\\ a\textsubscript{3}- a\textsubscript{2} = 4x - 2x = 2x\\                       

Since, the difference betweenthe successive terms is not same therefore it does not form an AP.

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