Find the n'th term of the sequence :
a) 1/2, 2/3, 3/4, 4/5
b) 5/1^2, 5/2^2, 5/3^2, 5/4^2
c) 3/1, 4/2, 5/3, 6/4
To find the n'th term of a sequence, we first need to identify the pattern or rule that governs the sequence.
a) Sequence: 1/2, 2/3, 3/4, 4/5
Observing the sequence, we can notice that the numerator increases by 1 and the denominator increases by 1 for each subsequent term. Therefore, the general pattern can be written as:
Term(n) = (n + 1) / (n + 2)
b) Sequence: 5/1^2, 5/2^2, 5/3^2, 5/4^2
In this sequence, the denominator represents the square of the natural numbers. The general pattern can be written as:
Term(n) = 5 / (n^2)
c) Sequence: 3/1, 4/2, 5/3, 6/4
Here, both the numerator and the denominator increase by 1 for each subsequent term. Therefore, we can write the general pattern as:
Term(n) = (n + 3) / (n + 1)
Now, using the respective formulas derived above, we can find the n'th term of each sequence:
a) To find the n'th term of the sequence 1/2, 2/3, 3/4, 4/5, plug the value of n into the formula:
Term(n) = (n + 1) / (n + 2)
b) To find the n'th term of the sequence 5/1^2, 5/2^2, 5/3^2, 5/4^2, plug the value of n into the formula:
Term(n) = 5 / (n^2)
c) To find the n'th term of the sequence 3/1, 4/2, 5/3, 6/4, plug the value of n into the formula:
Term(n) = (n + 3) / (n + 1)