1)Given

\(un+1=7−2un\)

\(u_{2}=5\)

Determine \(u_{1}\)

Let us evaluate the recurrence relation \(un+1=7-2un\) at \(n=1\)

\(u_{2}=7-2u_{1}\)

Since \(u_{2}=5\) has been given: \(5=7-2u_{1}\)

Subtract 7 from each side: \(5-7=7-2u_{1}-7\)

Combine like terms: \(-2=-2u_{1}\)

Divide each side by -2: \(\displaystyle-\frac{{2}}{{-{{2}}}}=-{2}{u}\frac{{1}}{{-{{2}}}}\)

Evaluate: \(1=u_{1}\)

Thus we then obtained \(u_{1}=1\)

2)Determine \(u_{0}\)

Let us evaluate the recurrence relation \(un+1=7-2un\) at \(n=0\)

\(u_{1}=7-2u_{0}\)

Since \(u_{2}=5\) has been given: \(1=7-2u_{0}\)

Subtract 7 from each side: \(1-7=7-2u_{0}-7\)

Combine like terms: \(-6=-2u_{0}\)

Divide each side by -2: \(\displaystyle-\frac{{6}}{{-{{2}}}}=-{2}{u}\frac{{0}}{{-{{2}}}}\)

Evaluate: \(3=u_{0}\)

Thus we then obtained \(u_{0}=3\).