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  • Find the rth term of an A.P. sum of whose first n terms is 2n+ 3n^2. [Hint: an = S_n - S_n-1]

Find the rth term of an A.P. sum of whose first n terms is 2n + 3n^2.

[Hint: a\textsubscript{n} = S\textsubscript{n} - S\textsubscript{n-1}]

Answers (1)

Sum of first n terms is given by S_n=2n + 3n^2

The rth term is    

\\a_{r}=S_{r}-S_{r-1}= \left( 2r+3r^{2} \right) - \left( 2 \left( r-1 \right) +3 \left( r-1 \right) ^{2} \right) \\\\ =2r+3r^{2}- \left( 2r-2+3r^{2}-6r+3 \right) \\\\ =2r+3r^{2}- \left( 3r^{2}-4r+1 \right) \\\\ =6r-1 \\\\

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infoexpert21

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