Odds, Evens and More Evens

Odds, Evens and More Evens printable worksheet
 

Here are the first few sequences from a family of related sequences:
 
$A_0 = 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29...$
 
$A_1 = 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42...$
 
$A_2 = 4, 12, 20, 28, 36, 44, 52, 60...$
 
$A_3 = 8, 24, 40, 56, 72, 88, 104...$
 
$A_4 = 16, 48, 80, 112, 144...$
 
$A_5 = 32, 96, 160...$
 
$A_6 = 64...$
 
$A_7 = ...$
 
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Which sequences will contain the number 1000?
 
Once you've had a chance to think about it, click below to see how three different students began working on the task.
 
Alison started by thinking:

Bernard started by thinking:

 
Charlie started by thinking:

Can you take each of their starting ideas and develop them into a solution?

Here are some further questions you might like to consider:
 
How many of the numbers from 1 to 63 appear in the first sequence? The second sequence? ...  
 
Do all positive whole numbers appear in a sequence?
Do any numbers appear more than once?
Which sequence will be the longest?  
 
Given any number, how can you work out in which sequence it belongs?
How can you describe the $n^{th}$ term in the sequence $A_0$? $A_1$? $A_2$? ... $A_m$?