tn=t1+(n-1)d=20-3(n-1)/2=(43-3n)/2.
Sn=108½=217/2.
Sn=t1+t2+t3+...+tn=(43-3)/2+(43-6)/2+...=43n/2-(3/2)(1+2+...+n)=43n/2-(3/2)n(n+1)/2.
43n/2-(3/2)n(n+1)/2=217/2,
86n-3n(n+1)=434,
83n-3n2=434,
3n2-83n+434=0=(n-7)(3n-62), so n=7 (because n must be an integer).