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In an AP, If S(n)=3n^(2)+5n and a(k)=164...

In an AP, If `S_(n)=3n^(2)+5n` and `a_(k)=164,` then find the value of k.

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`S_(n)=3n^(2)+5n`
` rArr S_(n-1)=3(n-1)^(2)+5(n-1)`
`=3(n^(2)-2n+1)+5(n-1)=3n^(2)-n-2`
Now, `a_(n)=S_(n)-S_(n-1)`
`=(3n^(2)+5n)-(3n^(2)-n-2)=6n+2`
`rArr a_(k)=6k+2`
Given that,` a_(k)=164`
`rArr 6k+2=164`
`rArr 6k=162`
`rArr k=27`
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