So my 11 year old son asked me for some help on his math homework yesterday. The questions he was having problems with are all number pattern problems (a simple example: 1,2,4,8,16,? Whats the next number in the pattern?). 5 out of 6 were easy to decipher, no big deal. The 6th has resisted the 45 minutes I’ve spent peering at it. I already sent him to school with a large question mark in the place of that question on his homework so don’t worry that you’ll be doing my 5th grader’s homework for him. In any case this problem (assuming it’s not a typo in the book) seems to be way out of the league of your run of the mill 11 year old. So help me out here Dopers. What are the missing numbers to the following sequence (X’s indicate numbers that need to be filled in to complete the pattern)?
I sure don’t see it… The numbers appear to be derived by taking the previous number, and multiplying it by 2, by 1.5, or by 1.25, but I don’t see a pattern.
Good work Q.E.D.. Now that it’s been shown to me it seems so simple. Seems like that’s the way it always is though with these types of problems… <grumble>
The problem with number patterns like this is that, in fact, we could come up with lots of formulas. In fact, there is a theorem in number theory that, given any sequence of real numbers x[sub]1[/sub], x[sub]2[/sub], x[sub]3[/sub], … x[sub]n[/sub], and any real number y, you can find a formula so that x[sub]n+1[/sub] = y.
OK, if it’s a sequence of odd numbers, the next number is 9.
If it’s a sequence of odd prime numbers, the next number is 11.
And if it’s a sequence of numbers that have the letter “e” in their alpha-name, then the next number is 8.
True that there are often many correct solutions, and a good grader will give credit for any of them, as long as they’re not too contrived. However, it is often the case that there is one simplest solution. As long as you acknowledge that you’re looking for the best solution, and not the only solution, I don’t mind these kind of things on standardized tests and the like.
<< a good grader will give credit for any of them, as long as they’re not too contrived…it is often the case that there is one simplest solution. As long as you acknowledge that you’re looking for the best solution…>>
And which is the “best” solution or the “simplest” solution to the sequence 1, 3, 5, 7… that I posed above?
Bah, I say, humbug. People who pose these kind of questions on tests are people who don’t understand mathematics. Or people who penalize students who think deeper than others.
And I strongly disagree that “a good grader” will give credit for blah blah. Most graders of these questions are computers, who read only a “right” answer. And most teachers who pose these questions don’t ASK the students to EXPLAIN their answer, they just ask “what comes next.”
Well, if my only choices are 47 and 64, I’m in trouble. I would have to go with 49 for either one. You do realize that those two algorithms produce the same sequence, right?
As for the other sequence you gave, I would say 9. Odd number is a simpler concept than odd prime number.
Wait a minute, what the heck? I swear when I quoted that, it said 47, not 49. I guess I’m just not reading very carefully. Sorry. But 49 is still the right answer, either way.