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\text{(ii) }a_2 = 27 > 10^1 \implies a_3 > (10^1)^3 = 10^3 \implies a_4 > 10^9 \implies a_5 > 10^27 \\[br]\implies a_6 > 10^{81} \implies a_7 > 10^{343} > 10^{100}
\dislaystyle u^2 = C - \frac{g}{k}
\displaystyle C = -\frac{g/k}\left(u^2k/g + 1\right)
\displaytyle y = \ln (r + s)