#### shastri.chandoo

##### New member

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Find the missing # in the series: 65, 33, _, 9

- Thread starter shastri.chandoo
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Find the missing # in the series: 65, 33, _, 9

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Too few data points to pin it down. You need infinitely many. Three is no good and ANY answer would only be guessing.

I'm pretty fond of 43/3. -- Nice, level second differences.

Of course, many such sequences are not mathematical at all. Maybe it's the number of overdrawn accounts at the 14th street credit union on the west side of Wyomissing, PA.

Unless you can provide additional information, that's sort of where we are.

I'm pretty fond of 43/3. -- Nice, level second differences.

Of course, many such sequences are not mathematical at all. Maybe it's the number of overdrawn accounts at the 14th street credit union on the west side of Wyomissing, PA.

Unless you can provide additional information, that's sort of where we are.

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But

A question like this is not really a math problem, but a psychological test: do you see the same shape in this ink blot as the author did? People familiar with certain types of math are likely to see the same thing, but that doesn't really make it more

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Thank you.

The answer is 17

The answer is 17

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Mark, don't worry as things are always weird looking for Denise.Gets kinda weird using Mark's formula:

65, 33, 17 ,9 ,5 ,3 ,2 , 3/2, 5/4, 9/8, 17/16, ....

I myself prefer to think that a

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\(\displaystyle 2a_{n+2}-3a_{n+1}+a_{n}=0\)

Then it's easy to see that the characteristic roots are:

\(\displaystyle r\in\left\{\frac{1}{2},1\right\}\)

And so the closed-form will be:

\(\displaystyle a_n=c_12^{-n}+c_2\)

Then we use known values to determine the parameters:

\(\displaystyle a_1=c_12^{-1}+c_2=65\implies c_1+2c_2=130\)

\(\displaystyle a_2=c_12^{-2}+c_2=33\implies c_1+4c_2=132\)

Solving this system, we find:

\(\displaystyle \left(c_1,c_2\right)=\left(2^7,1\right)\)

Hence:

\(\displaystyle a_n=2^7\cdot2^{-n}+1=2^{7-n}+1\)

There is noThank you.

The answer is 17

That is a plausible answer out of an infinitude of possible answers.

[in-

an infinite extent, amount, or number.

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That gives this pattern:Try a_{n}= (20/3)n^2 - 52n + 331/3

n

1-3: 65, 33, 14 1/3

4-6: 9, 17, 38 1/3

7-9: 73, 121, 182 1/3

10-12: 257, 344, 446 1/3

13-15: 561, 689, 830 1/3

and so on...

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You finally learned how to use a dictionary. Good for you! You have come so far since coming to this forum. I think that you are ready to solo, SO GO AWAY!infinitude

[in-fin-i-tood, -tyood]

infinity: divinenoun

an infinite extent, amount, or number.