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Question
The nth term of a sequence is given by an = 2n2 + n + 1. Show that it is not an A.P.
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Solution
We have:
an = 2n2 + n + 1
\[a_1 = 2 \times 1^2 + 1 + 1 \]
\[ = 4, \]
\[ a_2 = 2 \times 2^2 + 2 + 1\]
\[ = 11\]
\[ a_3 = 2 \times 3^2 + 3 + 1 \]
\[ = 22 \]
\[ a_2 - a_1 = 11 - 4 \]
\[ = 7\]
\[ \text { and } a_3 - a_2 = 22 - 11 \]
\[ = 11\]
\[\text { Since }, a_2 - a_1 \neq a_3 - a_2 \]
\[\text { Hence, it is not an AP } .\]
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