what is a possible explicit rule for the nth term of the sequence: 1/3, 1/2, 3/5, 2/3, 5/7?
Accepted Solution
A:
This one is a bit tricky, but a really important trick with fractions is that they can be written in different ways. For example, 1/2 = 2/4. This is the trick that this question wants you to see:
1/3, 1/2, 3/5, 2/3, 5/7 is the same as 1/3, 2/4, 3/5, 4/6, 5/7
It is then much easier to see that a possible rule is n/(n+2) since the denominator in this pattern is always 2 more than the numerator.