Question

The start of a sequence is (4)/(5),(5)/(6),(6)/(7),(7)/(8),dots What is the nᵗʰ term rule for this sequence? Give your answer as a fraction in its simplest form.

Answer 1

The nth term rule for this sequence is: (n+1)/(n+2)

To find the nth term rule, we need to identify a pattern that relates the term number (n) to the value of the term.

Observing the pattern:

The first term is 4/5, which can be written as (3+1)/(3+2).

The second term is 5/6, which can be written as (4+1)/(4+2).

The third term is 6/7, which can be written as (5+1)/(5+2).

And so on.

Generalizing the pattern:

We can see that the nth term has a numerator of n+1 and a denominator of n+2.