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We have to find a rational number between $7$ and $8$. Rational numbers are the numbers which are written in the form $\dfrac{p}{q}$ where $(q \ne 0)$.

So to find a rational number we add the first term $7$ and second term $8$ and divide it by $2$.

Then we get, \[\dfrac{{7 + 8}}{2} = \dfrac{{15}}{2} \Rightarrow 1^{st}\] rational number.

\[2^{nd}\] rational number \[\dfrac{{\dfrac{{15}}{2} + 8}}{2} = \dfrac{{\dfrac{{15 + 16}}{2}}}{2} = \dfrac{{31}}{4}\].

\[3^{rd}\]rational number \[\dfrac{{\dfrac{{31}}{4} + 8}}{2} = \dfrac{{\dfrac{{31 + 32}}{4}}}{2} = \dfrac{{63}}{8}\].

And so on.