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Find te rth term of an AP sum of ...

Find te rth term of an AP sum of whose first n terms is `2n+3n^(2).`

Text Solution

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Given that sum of n terms of an AP.
`S_(n)=2n+3n^(2)`
` T_(n)=S_(n)-S_(n-1)`
`=(2n+3n^(2))-[2(n-1)+3(n-1)^(2)]`
`=(2n+3n^(2))-[2n-2+3(n^(2)+1-2n)]`
` =(2n+3n^(2))-(2n-2+3n^(2)+3-6n)`
`=2n+3n^(2)-2n+2-3n^(2)-3+6n`
` =6n-1`
`rth "term " T_(r)=6r-1`
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