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 2021-06-26

A sequence is generated by the recurrence relation \(u_n+1=7-2u_n\)
If \(u_2=5\), what is the value of \(u_0\)?

Expert Answers (1)

2021-06-27

1)Given
\(u_n+1=7-2u_n\)
\(u_2=5\)
Determine \(u_1\)
Let us evaluate the recurrence relation \(u_n+1=7-2u_n\) 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: \(\frac{-2}{-2}=\frac{-2u_1}{-2}\)
Evaluate: \(1=u_1\)
Thus we then obtained \(u_1=1\)
2)Determine \(u_0\)
Let us evaluate the recurrence relation \(u_n+1=7-2u_n\) 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: \(\frac{-6}{-2}=\frac{-2u_0}{-2}\)
Evaluate: \(3=u_0\)
Thus we then obtained \(u_0=3\)

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