Question

Here are the first four terms of some sequence.

1/2 , 4/3 , 9/4 , 16/5
Find the nth term of this sequence

Answer 1

The nth term of the sequence will be: n²/n+1

Explanation:

Given the sequence

1/2 , 4/3 , 9/4 , 16/5

The values in the numerator are:

2, 3, 4, 5

It is clear that every successive value in the numerator can be determined by adding 1 to the previous value.

i.e.

3 = 2+1

4 = 3+1

5 = 4+1

Thus, the nominator contains the sequence rule: n+1

The values in the denominator are:

1, 4, 9, 16

It is clear that every value in the denominator is the square of the sequence number.

i.e.

1 = 1²

2 = 2²

3 = 3²

4 = 4²

5 = 5²

so

The denominator defines the rule n².

Thus, the nth term of the sequence will be: n²/n+1