\[a_{n} = 7 + 3n = 10 + 3n - 3 =\]
\[= 10 + (n - 1) \cdot 3 \Longrightarrow a_{1} = 10;\ \ \]
\[d = 3.\]
\[S_{20} = \frac{2a_{1} + (20 - 1)d}{2} \cdot 20 =\]
\[= \frac{2 \cdot 10 + 19 \cdot 3}{2} \cdot 20 =\]
\[= (20 + 57) \cdot 10 =\]
\[= 77 \cdot 10 = 770.\]