Nth term fraction

Question

1/3,

2/5,

3/7,

4/9

 

A) what are the next three terms of this sequence?

B) find an expression for the nth term of this sequence?

Answer 1

A

1/3, 2/5, 3/7, 4/9,

the fifth term is 5 over the next odd number: 5/11

then comes 6/13 and 7/15

B

n/(2n+1)

Answer 2

1/3,  2/5,  3/7,  4/9

 

Notice how the numerator increases:    1, 2, 3, 4, ...

And how the denominator increases:     3, 5, 7, 9

 

So, if the first term is a₁,

   we can write an expression to determine any term:

 

b)      a_n = n / (2n+1)                    [expression for n^th term]

 

a) the next three terms are (likely):

         a₅ = 5 / (2*5+1) = 5/11

         a₆ = 6 / (2*6+1) = 6/13

         a₇ = 7 / (2*7+1) = 7/15