I had the following on a daily calendar I use, but I arrived at my answer differently than they did:
I’m just curious to see if the rest of you come up with their answer or mine.
I get 91. The numbers in the sequence go up by 18.
Same answer as Stainz, different reasoning.
Each pair of numbers adds up to 10
I should have said, I want to see if you come up with the same rationale that they used.
At any rate, Stainz, you came about it the same way I did. However, their explanation…
…was much simpler: “Two series. 1, 3, 5, 7, 9 and the same sequence reversed.” I didn’t notice that pattern at all until reading their solution.
The first thing I thought of was…a palindrome. The same sequence backwards and forwards, the last number has to be 1.
[QUOTE=Jayn_Newell]
Same answer as Stainz, different reasoning.
Each pair of numbers adds up to 10
[/QUOTE]
Huh…didn’t even think of that one, although that’s closer to what the calendar’s answer is.
Robot Arm, apparently you should be authoring these puzzles. 
I get 91, because the first difference is constant (basically the same as what Stainz said, but with extra jargon).
Without looking at the other answers:
the next number is 1. The first number is decreasing by 2 and the second number is increasing by 2. You could do a more complicated solution, like the first number increases by 2 and the first plus the second number = 10.
Hey, I got the right answer and a unique solution! Yay me! I never get these.
Asimovian, I solved it the same way you did. I think your strategy is the first one I try with any sequence puzzle.
Daniel
i got it by doubling the number, then adding the previous. eg 73 = 2 x 55 - 37
[QUOTE=Spidey]
i got it by doubling the number, then adding the previous. eg 73 = 2 x 55 - 37
[/QUOTE]
Wow…that’s a different one – I like it! 
How would you get the second number in the sequence, though? In other words, 37 = 2 x 19 - ??
without looking at anybody else’s reply, the final number is 91, which makes the series a palindrome.
I like the cut of your jib, pat.
I also jumped to the palindrome solution. Normally I’ll first check first and second differences for these, but this one was so obviously a palindrome.
I got the same answer as everyone else, but with different reasoning.
I couldn’t help but notice that the first four terms are the values of
n^5 - 15n^4 + 85n^3 - 225n^2 + 292n - 199
for n = 1, 2, 3, 4. Evaluating at n=5 gives 91.
My first thought was the same as Robot Arm’s. After looking for an alternative solution, I came up with Stainz’s.
But before any of that, I was thrown off a little because, technically, what we’re finding is not a number but a digit. If we really were looking for the next number in the sequence 19 - 37 - 55 - 73 - 9, some of these solutions (like Stainz’s), won’t work.
I also figured that the first four numbers were
1x18+1
2x18+1
3x18+1
4x18+1
and the next one should be
5x18+1
but like Thudlow, I missed that the question was asking for a digit not a new number.
I also missed
the palindrome pattern
Did anyone come up with a different answer?
I got to the 9? at the end and thought, huh? But I did the same as other people. I found the constant difference to be 18. Then I noticed that it was a palindrome.
[QUOTE=Otto]
Hey, I got the right answer and a unique solution! Yay me! I never get these.
[/QUOTE]
Cool! This is how I figured it out, too–but you were still first!