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  • Justify whether it is true to say that the following are the nth terms of an AP. 1+n+n^2

Justify whether it is true to say that the following are the nth terms of an AP. 1+n+n^2

Answers (1)

Answer.          [No]

Solution.        

\text{Here } a_{n} = 1 + n + n^{2} \\ \text{Put } n = 1, \quad a_{1} = 1 + 1 + (1)^{2} = 3 \\ \text{Put } n = 2, \quad a_{2} = 1 + 2 + (2)^{2} = 7 \\ \text{Put } n = 3, \quad a_{3} = 1 + 3 + (3)^{2} = 13 \\ \text{The numbers are } 3, 7, 13, \ldots \\ a_{2} - a_{1} = 7 - 3 = 4 \\ a_{3} - a_{2} = 13 - 7 = 6 \\

Here common difference is not same

Hence 1 + n + n^2  is not the nth term of an AP.

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infoexpert21

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