(a)[4]
The first two terms of an arithmetic progression are $16$ and $24$. Determine the smallest number of terms from the progression that need to be included so that their sum is greater than $20\,000$.
(b)[4]
A geometric progression has first term $6$ and sum to infinity $18$. A new geometric progression is created by squaring every term of the original progression. Determine the sum to infinity of the new progression.