Question

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

Equation, expression, and inequalitie

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

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 $$u_0=3$$