Question

A sequence is generated by the recurrence relationun+1=7−2unIf u2=5, what is the value of u0?

Equation, expression, and inequalitie
ANSWERED
asked 2021-06-23

A sequence is generated by the recurrence relation \(un+1=7−2un\)
If \(u_{2}=5\), what is the value of \(u_{0}\)?

Answers (1)

2021-06-24

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 \(u_{0}=3\).

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