(a(i))[2]
A cyclist takes part in a long-distance charity ride across Africa. The overall distance is $3050\,\text{km}$. He begins on May $1$st and rides $200\,\text{km}$ that day. After that, the distance he rides each day goes down by $5\,\text{km}$. How far will he travel on May $15$th?
(a(ii))[3]
On which date will he finish the event?
(b(i))[4]
A geometric progression has third term equal to $8$ times the sixth term, and the sum of the first six terms is $31\frac{1}{2}$. Determine the first term of the progression.
(b(ii))[1]
Find the sum to infinity of the progression.