NRICH: Odds, Evens and More Evens
Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions…
Here are the first few sequences from a family of related sequences:
A0=1,3,5,7,9,11,13,15,17,19,21,23,25,27,29…
A1=2,6,10,14,18,22,26,30,34,38,42…
A2=4,12,20,28,36,44,52,60…
A3=8,24,40,56,72,88,104…
A4=16,48,80,112,144…
A5=32,96,160…
A6=64…
A7=...
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.
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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 nth term in the sequence A0? A1? A2? … Am?
Age 11 to 14
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Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions…
Here are the first few sequences from a family of related sequences:
A0=1,3,5,7,9,11,13,15,17,19,21,23,25,27,29…
A1=2,6,10,14,18,22,26,30,34,38,42…
A2=4,12,20,28,36,44,52,60…
A3=8,24,40,56,72,88,104…
A4=16,48,80,112,144…
A5=32,96,160…
A6=64…
A7=...
.
.
.
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 nth term in the sequence A0? A1? A2? … Am?
Age 11 to 14