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  • Which of the following form an AP? Justify your answer. 2, 2^2, 2^3, 2^4, ...

Which of the following form an AP? Justify your answer. 2, 2^2, 2^3, 2^4, ...

Answers (1)

Answer.          [No]

Solution.        

\text{Here the given series is } 2, 2^2, 2^3, 2^4, \ldots \\\text{ where } a_1 = 2, \quad a_2 = 2^2, \quad a_3 = 2^3, \quad a_4 = 2^4 \\ a_2 - a_1 = 2^2 - 2 = 4 - 2 = 2 \\ a_3 - a_2 = 2^3 - 2^2 = 8 - 4 = 4 \\ a_4 - a_3 = 2^4 - 2^3 = 16 - 8 = 8 \\

 

Here the difference of the successive terms is not same. Hence it is not an AP.

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