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If the sum of n terms of a sequence ...

If the sum of n terms of a sequence is quadratic expression it always represents an AP.

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False
`"let "S_(n) =an^(2)+bn+c`
`S_(1)=a+b+c`
`a_(1)=a+_b+c`
` S_(2) =4a+2b+c`
`therefore a_(2) =S_(2)-S_(1) `
`=4a+4b+c-(a+b+c)=3a+b`
` s_(3) =9a+3b+c`
` therefore a_(3) =S_(3) -S_(2) =5a+b`
`Now , a_(2)-a_(1) =(3a+b)-(a+b+c)=2a-c`
`a_(3) -a_(2) =(5a+b)-(a+bc)=2a-c`
`now a_(2) -a_(1) ne a_(3)-a_(2) `
hence , the statement is false .
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