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

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.