SOLUTION: I have a question on this; I have tried multiple times, but cannot find the answer. Can you help?
The question is:
What is the value of the missing number?
5, 9, 16, 29, 54,
Algebra.Com
Question 999402: I have a question on this; I have tried multiple times, but cannot find the answer. Can you help?
The question is:
What is the value of the missing number?
5, 9, 16, 29, 54, (missing number), 200
If you could explain this, that would be awesome. Thanks!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
If you need an integer value, I confess myself stumped. But I did find a rational number value that fits a 5th-degree polynomial model of these data.
A degree 5 polynomial has the form:
\ =\ a_0x^5\ +\ a_1x^4\ +\ a_2x^3\ +\ a_3x^2\ +\ a_4x\ +\ a_5)
Mapping the set 
to your data set and fitting it to the polynomial model, we get:
^5\ +\ a_1(0)^4\ +\ a_2(0)^3\ +\ a_3(0)^2\ +\ a_4(0)\ +\ a_5\ =\ 5)
^5\ +\ a_1(1)^4\ +\ a_2(1)^3\ +\ a_3(1)^2\ +\ a_4(1)\ +\ a_5\ =\ 9)
^5\ +\ a_1(2)^4\ +\ a_2(2)^3\ +\ a_3(2)^2\ +\ a_4(2)\ +\ a_5\ =\ 16)
^5\ +\ a_1(3)^4\ +\ a_2(3)^3\ +\ a_3(3)^2\ +\ a_4(3)\ +\ a_5\ =\ 29)
^5\ +\ a_1(4)^4\ +\ a_2(4)^3\ +\ a_3(4)^2\ +\ a_4(4)\ +\ a_5\ =\ 54)
^5\ +\ a_1(6)^4\ +\ a_2(0)^3\ +\ a_3(6)^2\ +\ a_4(6)\ +\ a_5\ =\ 200)
Which simplify to:
Since the value of 
is discernable by inspection (the reason for my selection of 0 for the first element of the domain set), this 6X6 system can be quickly reduced to the 5X5 system:
You can use any of the myriad matrix solvers found online to find the solution to this system, and then once you have the 6 coefficients of your 5th-degree polynomial, you can evaluate )
to find your missing number.
My coefficient set came out to be 
and I got \ =\ \frac{207}{2})
John
My calculator said it, I believe it, that settles it
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