How many terms of the series 54,51, 48,.. be taken so that their sum is 513? Explain the double answer

Explanation

`a=54`

`d=−3`

`S_ n` `=513`

`S_n` = `n/2` `(2a+(n−1)d)`

`513= ``n/2` `(108+3−3n)`

`1026=111n−``3n^2`
`n^2``−37n+342=0`

`(n−18)(n−19)=0`

on solving, we get
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