Justify whether it is true to say that the sequence, having follo… - Vidyadip

Question

Justify whether it is true to say that the sequence, having following $n ^{\text {th }}$ term is an A.P.
$a_n=1+n+n^2$.

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Answer

Consider the expression an $=1+n+n^2$,
For $n =1, a _1=1+1+1=3$
For $n=2, a_2=1+2+4=7$
For $n=3, a_3=1+3+9=13$
For $n=4, a_4=1+4+16=21$
The first four terms are $3,7,13,21$.
The difference between each consecutive term in not same.
Hence this is not an A.P.

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