Understanding sequencing and fraction differences.

Context: It would normally follow on from work on sequences and fractions

Question: Ruth was investigating fraction differences. She wrote down this sequence of fractions:

1/1, 1/2, 1/3, 1/4, 1,5 1,6 ... ...

Then she worked out the difference between the consecutive fractions:

1/2, 1/6, 1/12, 1/20, 1/30, .. ..

She Then worked out the differences between the Fractions in her second series.

1/3, 1/12 ... ...

Investigate Further:

When doing this question make sure your look at these three things,

1. Making and monitoring decions to solve problems.
2.Communicating mathematically.
3.Developing skills of mathematical reasoning.

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Solution Preview

... 4,6,8,10,... is easily seen and can be continued to produce the next numbers in the sequence
<br>1/2, 1/6, 1/12, 1/20, 1/30, 1/42, 1/56,...
<br>by adding in the denominator, without using the more difficult method of subtracting the elements from the first sequence.
<br>
<br>The next sequence,
<br>1/3, 1/12, ...
<br>is too short to draw conclusions. I might guess that, since the difference between the denominators is 12-3=9, the next denominator might be 12+(9+4) or something like that, but I will have to make the ...