Question 976760
{{{S[n]=(n/2)(2a[1]+(n-1)d)}}}

let's enter what we were given - 

{{{63=(n/2)(42-4(n-1))}}}


{{{63=(n/2)(46-4n))}}}

{{{126=(46n-4n^2))}}}

{{{4n^2-46n+126=0}}}

{{{2n^2-23n+63=0}}}

I'd use the quadratic equation here, note, the solutions result in 4.5 and 7, but the answer must be an integer. 

{{{n=7}}}