(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Dang it! More recurrence relation problems, but this time it’s due to a quadratic equation.

Q.In the sequence u_{1}, u_{2}, u_{3},…,u_{n},

u_{1}= 0, u_{2}= 3, u_{3}= 12 and u_{n}= a + bn + cn^{2}

Find the values of a, b and c.

2. Relevant equations

Provided at back of book…

Answer: a = 3, b = -6, c = 3

3. The attempt at a solution

Attempt:

If n = 1 then u_{1}= a + b(1) + c(1)^{2}= 0

= a + b + c = 0

If n = 2 then u_{2}= a + b(2) + c(2)^{2}= 3

= a + 2b + 4c = 3

If n = 3 then u_{3}= a + b(3) + c(3)^{2}= 12

= a + 3b + 9c = 12

Each value of u_{n}is a multiple of 3, hence the answers (a, b and c) are also multiples of 3, so I’m guessing that I need to use some kind of ratio solution between each new quadratic to find the answer. The difficulty I’m having is that other quadratic equations I’ve solved for already had values for the coefficients, so I’m uncertain on what quadratic formula I need at this point. I probably don’t need one, but I’m definitely stuck either way.

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# Quadratic Recurrence Relation

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