Please find the sum.

we see that the first term=a=54

common diff =d=-3

let the sum of n terms is 513

so using the formula we get,

n/2[2a+(n-1)d]=513

putting the values of a and d,we get a quadraticc equation, on factorising that

 we get,

(n-18)(n-19)=0

so

n=18

or

n=19

so if the number of terms is 18 or 19, we get the sum as zero.

now, for the double answer

since the 18th term

=a+17d

=54+17(-3)

=3

since the common diff is -3,

the next term i.e.the 19th term will be

3+(-3)=0

so whethter you take the sum of 18 terms or 19 terms , it will still be 513

as the 19th term is zero.