[tex]\displaystyle \\
\frac{3^{n-1}\times 7^{n+1}}{21^n} =\\ \\
=\frac{3^{n-1}\times 7^{n-1+2}}{21^{n-1+1}} =\\ \\
=\frac{3^{n-1}\times 7^{n-1}\times 7^2}{21^{n-1}\times21^1} =\\ \\
=\frac{(3\times 7)^{n-1} \times 49}{21^{n-1}\times21} =\\ \\
=\frac{21^{n-1} \times 49}{21^{n-1}\times21} = \frac{49}{21}= \boxed{\frac{7}{3}}[/tex]
