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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.

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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