Answer:
The nth term of the sequence will be: n²/n+1
Step-by-step 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
