Question

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

Answers (1)

2021-06-27
1)Given
un+1=7−2un
u2=5
Determine u1
Let us evaluate the recurrence relation un+1=7-2un at n=1 u2=7-2u1
Since u2=5 has been given: 5=7-2u1
Subtract 7 from each side: 5-7=7-2u1-7
Combine like terms: -2=-2u1
Divide each side by -2: \(-2/-2=-2u1/-2\)
Evaluate: 1=u1
Thus we then obtained u1=1
2)Determine u0
Let us evaluate the recurrence relation un+1=7-2un at n=0 u1=7-2u0
Since u2=5 has been given: 1=7-2u0
Subtract 7 from each side: 1-7=7-2u0-7
Combine like terms: -6=-2u0
Divide each side by -2: \(-6/-2=-2u0/-2\)
Evaluate: 3=u0
Thus we then obtained u0=3.
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