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The nth term of a sequence is given by a...

The nth term of a sequence is given by `a_n=2n^2+n+1.` Show that it is not an A.P.

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`a_n`=`2n^2``+n+1`
`a_1`=`2(1)^2``+(1)+1=4`
`a_2`=`2(2)^2``+(2)+1=11`
`a_3`=`2(3)^3``+(3)+1=21`
Since,`a_3`−`a_2`≠`a_2`−`a_1`
∴ The given sequence is not as A.P. as consecutive terms do not have a common difference.
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