Sort these infinite sequences into groups. (They are available on cards for cutting out.)
- How will you choose to define the groups?
- Are there some sequences which belong to more than one group?
Once you have sorted the sequences into groups, write a further sequence for each group.
How else could you have sorted the sequences?
\(\dfrac12, -\dfrac{1}{4}, \dfrac18, -\dfrac{1}{16}, ...\)
\(3\sqrt2, 4\sqrt2, 5\sqrt2, 6\sqrt2,...\)
\(2,0,-2,-4,...\)
\(\ln 1, \ln 2, \ln 3, \ln 4, ...\)
\(-1, -\sqrt2, -2, -2\sqrt2, ...\)
\(1,1,1,1,...\)
\(1, \dfrac12, \dfrac13, \dfrac14, ...\)
\(-1, 1, -1, 1, ...\)
\(0.1, 0.01, 0.001, 0.0001, ...\)
\(3,2\dfrac13, 1\dfrac23, 1,...\)
\(4, 8, 16, 32, ...\)
\(\cos\left(\frac{\pi}{4}\right), \cos\left(\frac{2\pi}{4}\right), \cos \left(\frac{3\pi}{4}\right), \cos\left(\frac{4\pi}{4}\right), ...\)
\(1, 1\dfrac12, 1\dfrac23, 1\dfrac34, ...\)
\(100, 105, 110, 115, ...\)
\(3.75, 5.625, 8.4375, 12.65625, ...\)
