MHB (Seemingly) Random Sequences

[Monoxdifly]

TL;DR Summary

Just some sequences which I don't know what are the next numbers.

Given a sequence 32, 16, 4, 18, 9, 3, .... The next numbers are ....
A. 17, 8, 5
B. 17, 6
C. 17, 4
D. 16, 4
E. 14, 8

My train of thought was to group the sequence into three numbers, so we get (32, 16, 4) and (18, 9, 3).
32 is two times of 16 which is square of 4.
18 is two times of 9 which is square of 3.
Following this logic, the third number of the third group should be 2, then the second number of the third group should be 4, and the first number of the third group should be 8. Thus, the next numbers should be 8, 4. However, it's not available in the options. Do you guys have any other idea how the pattern is supposed to be?

 

[PeroK]

I agree with you. These are, in fact, related to the quantum numbers associated with electron shells, in reverse order.

The maximim number of electrons in each shell is 2, 8, 18 32. Ignoring spin the numbers are 1,4, 9, 16. These correspond to the first, second, third and fourth shells.

 

[Mark44]

As far as I can tell, the sequences have nothing to do with quantum numbers or electron shells.

Of the choices given, the only one that seems reasonable to me is A., provided that what you wrote as 8, 5 was really 8,5. In the US we use a period as the separator between the integer part of a number and the fractional part, so we would write this number as 8.5. Many other countries use a comma for this purpose. Based on your IP address, you are not in the US, so perhaps in your country 8.5 would be written as 8,5.

The six numbers given appear to be in two triplets with each in the form of $N, \frac N 2, \sqrt {\frac N 2}$.
The only choice of the five given choices that follows this pattern is A, with its two numbers being 17 and $\frac {17} 2 = 8.5$, again under the proviso I wrote above.

The fact that choices B, C, D, and E list only two numbers is another reason for me to believe that there are only two numbers listed in choice A: 17 and 8.5.

 

[Monoxdifly]

I agree with you. These are, in fact, related to the quantum numbers associated with electron shells, in reverse order.

The maximim number of electrons in each shell is 2, 8, 18 32. Ignoring spin the numbers are 1,4, 9, 16. These correspond to the first, second, third and fourth shells.

Wait, so those seemingly random numbers in chemistry which made me give up on it was 2n² all along?

As far as I can tell, the sequences have nothing to do with quantum numbers or electron shells.

Of the choices given, the only one that seems reasonable to me is A., provided that what you wrote as 8, 5 was really 8,5. In the US we use a period as the separator between the integer part of a number and the fractional part, so we would write this number as 8.5. Many other countries use a comma for this purpose. Based on your IP address, you are not in the US, so perhaps in your country 8.5 would be written as 8,5.

The six numbers given appear to be in two triplets with each in the form of $N, \frac N 2, \sqrt {\frac N 2}$.
The only choice of the five given choices that follows this pattern is A, with its two numbers being 17 and $\frac {17} 2 = 8.5$, again under the proviso I wrote above.

The fact that choices B, C, D, and E list only two numbers is another reason for me to believe that there are only two numbers listed in choice A: 17 and 8.5.

After I rechecked the book this question was in, indeed there is no space after the second comma and as you guessed, I'm from a country which uses comma as decimal point, so it was indeed supposed to be 17, 8.5.

That said, what formula gives the sequence 32, 18, 17, ...?

 

[Mark44]

so it was indeed supposed to be 17, 8.5.

And the next number would be $\sqrt{8.5}$, assuming the pattern I described holds.

That said, what formula gives the sequence 32, 18, 17, ...?

No idea. I don't think this is enough information to be able to deduce a pattern.

 

[Office_Shredder]

@Mark44 this might be the most impressive deduction I have seen on this forum.

 

[Mark44]

@Mark44 this might be the most impressive deduction I have seen on this forum.

Aww, shucks!

 

[Monoxdifly]

And the next number would be $\sqrt{8.5}$, assuming the pattern I described holds.

No idea. I don't think this is enough information to be able to deduce a pattern.

All I could deduce was 32 = 8 × 4, 18 = 9 × 2, and 17 = 17 × 1, with the first factors forming Fibonacci sequence and the second factors forming a geometric sequence with 0,5 rasio. Thus, the next number in the sequence would be (9 + 17) × 0.5 = 26 × 0.5 = 13.

Anyway, here's another.
3, 7, 17, 38, 84
A. 181
B. 179
C. 177
D. 173
E. 170

If the terms are only 17, 38, 84, it would be easy, which is 17 × 1, 19 × 2, 21 × 4. However, the 3 and 7 didn't fit. Any idea for this one?