Answer :

The parts of the given question are solved below:

(a) We have,

,

We can observe that,

The numerator is a multiple of 3

And the denominator is a multiple of 5

Hence,

The next four rational numbers in this pattern are as follows:

… =

(i) Here, we have,

,

We can observe that,

The numerator and denominator are a multiple of increasing natural numbers.

Hence,

The next four rational numbers in this pattern are as follows:

, …

, …

(ii) Here, we have,

,

We can observe that,

The numerator and denominator are a multiple of increasing natural numbers.

Hence,

The next four rational numbers in this pattern are as follows:

, …

, …

(iii) Here, we have,

,

We can observe that,

The numerator and denominator are a multiple of increasing natural numbers.

Hence,

The next four rational numbers in this pattern are as follows:

, …

, …

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