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How many terms of the A.P. 54 ,51 , 48 …...

How many terms of the A.P. 54 ,51 , 48 …….. Are needed to give the sum 513 ?

Text Solution

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`a=54,d=-3,n=?S_(n)=513`
`S_(n)=(n)/(2)[2a+(n-1)d]rArr513=(n)/(2)[2(54)+(n-1)(-3)]`
`513xx2=n[108-3n+3]rArr1026=n[111-3n]`
`therefore1026=111n-3n^(2)rArr342=37n-n^(2)-37n+342=0`
`(n-18)(n-19)=0rArrn=18,19`.
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