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If the sum of n terms of an A . P is 3n^...

If the sum of n terms of an A . P is `3n^(2)+5n` and its `m^(th)` term is 164 , find the value of m.

Text Solution

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Given , `S_(n)=3n^(2)+5n`,
`thereforeS_(n-1)=3(n-1)^(2)+5(n-1)`
`thereforea_(n)=S_(n)-S_(n-1)=(3n^(2)+5n)-{3(n-1)^(2)+5(n-1)}`
`=(3n^(2)+5n)-[3(n^(2)-2n+1)+5n-5]`
`thereforea_(n)=6n-3+5=6n+2`, put n=m
`thereforea_(m)=6m+2rArr164`
`rArr6m=162rArrm=27`
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