Help with number sequencing

[melisalyn]

Hi! A friend of mine needs help with number sequencing. Her daughter is stuck! She needs the next three numbers in the sequence: 550, 226, 114, ...
I have tried everything I know to figure it out. I'm sure it's pretty obvious one the answer is known. Can someone help please? Thank you!!

Melissa

 

[tkhunny]

I REALLY hate these problems. There is NOT just one answer. There are INFINITELY MANY. You should produce a number you can live with and argue it. If it is marked wrong, cry foul to the highest level.

One possible solution, based on constant second differences, is 214, 526, 1050 - but so what!? There are INFINITELY many solutions. Really.

 

[mmm4444bot]

Hello Melissa:

Please ask your friend's daughter to come here herself and tell us why she is stuck.

It would also help, if she were to explain what her class is currently studying.

Thank you! :cool:

 

[soroban]

Hello, melisalyn!

Find the next three numbers in the sequence: 550, 226, 114, ...

The simplest is a quadratic function: .\(\displaystyle f(n) \:=\:106n^2 - 642n + 1086\)


Is there a typo?

If the first number is 450, there is a strong pattern.

Note that each term is about half of the preceding term.

\(\displaystyle \begin{array}{cccccc}a_1 &=& 450 \\ \\ [-4mm] a_2 &=& \frac{450}{2} + 1 &=& 226 \\ \\ [-4mm] a_3 &=& \frac{226}{2} + 1 &=& 114 \end{array}\)

Hence: .\(\displaystyle a_{n+1} \:=\:\frac{1}{2}a_n + 1\)

 

[tkhunny]

We've had this argument before. Time to expose it again? There is NOT a "simplest" because you cannot define it.

The simplest probably is the list 550, 226, 114, then there are no further entries in the list. That's only 11 characters compared to your 20!

"Simplest" cannot be defined in this context.

 

[mmm4444bot]

It's a moot point now, TK, as Soroban already provided camera-ready copy.

 

[tkhunny]

I've been at it this long. No need to take any other path.