Series Question (Sum to infinity) & Finding the smallest value

Question

I need help with part c) in the question shown in the image.

Series Question

Answer 1

$\sum_{n=k}^{\infty}u_n=u_k\sum_{j=1}^{\infty}(\frac{2}{3})^j=324\times (\frac{2}{3})^k=s_k$ Solve for $k$, from $s_k\le 2.5$, using logs.