If an AP starts with 3 and its first 20 terms total 1390, what is the common difference?

1390 = $\frac{20}{2}$$[2(3)+19d]=10[6+19d]$, so $139=6+19d$, giving $19d=133$ and $d=7$. The value 6.65 comes from using 20$d$ instead of 19$d$ in the bracket — 20 terms have only 19 gaps between them. 69.5 is the average term $\frac{1390}{20}$, not the step between terms. 5 fails the check, since $S_{20}$ would then be 1010.