Question: "A sequence is generated by the recurrence relation..."

High School
Algebra
Pre-Algebra
Equations, expressions, and inequalitie

FizeauV

Answered question

2021-06-26

A sequence is generated by the recurrence relation $u_{n} + 1 = 7 - 2 u_{n}$
If $u_{2} = 5$ , what is the value of $u_{0}$ ?

Answer & Explanation

Neelam Wainwright

Skilled2021-06-27Added 102 answers

1)Given
$u_{n} + 1 = 7 - 2 u_{n}$
$u_{2} = 5$
Determine $u_{1}$
Let us evaluate the recurrence relation $u_{n} + 1 = 7 - 2 u_{n}$ at n=1 $u_{2} = 7 - 2 u_{1}$
Since $u_{2} = 5$ has been given: $5 = 7 - 2 u_{1}$
Subtract 7 from each side: $5 - 7 = 7 - 2 u_{1} - 7$
Combine like terms: $- 2 = - 2 u_{1}$
Divide each side by -2: $\frac{- 2}{- 2} = \frac{- 2 u_{1}}{- 2}$
Evaluate: $1 = u_{1}$
Thus we then obtained $u_{1} = 1$
2)Determine $u_{0}$
Let us evaluate the recurrence relation $u_{n} + 1 = 7 - 2 u_{n}$ at n=0 u $1 = 7 - 2 u_{0}$
Since $u_{2} = 5$ has been given: $1 = 7 - 2 u_{0}$
Subtract 7 from each side: $1 - 7 = 7 - 2 u_{0} - 7$
Combine like terms: $- 6 = - 2 u_{0}$
Divide each side by -2: $\frac{- 6}{- 2} = \frac{- 2 u_{0}}{- 2}$
Evaluate: $3 = u_{0}$
Thus we then obtained $u_{0} = 3$

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