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

Equation, expression, and inequalitie
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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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