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  • State whether statement in True or False. If the sum of n terms of a sequence is quadratic expression then it always represents an A.P.

State whether statement in True or False.  If the sum of n terms of a sequence is quadratic expression then it always represents an A.P.

Answers (1)

S_{n}=an^{2}+bn+c \\\\

For n=1     S_{1}=a+b+c \\\\

   \\ S_{2}=4a+2b+c \\\\ S_{3}=9a+3b+c \\\\ a_{1}=S_{1}=a+b+c \\\\ a_{2}=S_{2}-S_{1}=3a+b \\\\ a_{3}=S_{3}-S_{2}=5a+b \\\\
    \\d=a_{2}-a_{1}=2a-c \\\\ d=a_{3}-a_{2}=2a \\\\ a_{3}-a_{2} \neq a_{2}-a_{1} \\\\

 

So, it does not represent an AP because common difference is not same.   

Posted by

infoexpert21

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