what is the next series of 1,10,3,9,5,8,7,7,9,6? And how did you figure it out?

Question

Can you tell me the next number series of the above? Also can you give me the outline as to how you discovered it?

Answer 1

Basically, there are 2 patterns occurring. The first one starts with the # 1. If you add 2 to that #, you get 3. Add 2 to that and you get 5... plus 2 is 7... So you can see that every other number follows the pattern of adding 2 to the previous # in that pattern.  The next pattern starts with 10. Every other number in that sequence follows the rule of subtracting 1 from the previous # in that pattern. So the next # would be 9, then 8, then 7, and so on. 

 

So... in order to find the next number in the sequence, we must look two numbers back and determine the pattern.  The last number is 6, and we got to that point by subtracting 1. The number before that, which is the one that will impact the next number, is 9. We got that number by adding 2. So if we add 2 to that, we get 11. Eleven is the next number in the sequence. Continue likewise to find additional numbers in the sequence. 

Answer 2

Now, whatever you do, allow improvements to this procedure, but don’t let anyone tell you, “just try any approach until you find one that works” --- always, describe it as a procedure (with a “rule”).

PLZ do some study on this topic at:
     http://www.mathsisfun.com/algebra/sequences-finding-rule.html
     http://www.purplemath.com/modules/nextnumb.htm

The given problem interleaves (now, there’s a big word) two sequences into one (odd and even positions).  Once you see that pattern (or rule or procedure), the answer is obvious.  But, what do you do next time?  That’s where a procedure is important.

Special note:  With a very short sequence, there are many rules that apply, but they each generate a unique next value.  As a sequence gets longer and longer, fewer and fewer rules apply.

Here’s my classic example:  What’s the next letter in this sequence?   M V E M J S U N

Note: Microsoft has put several such sequences into Office programs like Excel so that the software automatically extends a sequence (like January, February, March, …)

Answer 3

Hello Renee,

 

 There are two things at work here. First of all, the second, fourth, sixth, etc. numbers in the series are simply 10,9,8,7...etc.     The first, third, fifth, etc numbers in the series are 1,3,5,7,9...etc. So, if the series were to continue, it would be

 

 11,5,13,4,15,3,17,2,19,1   (and possibly more)