(a)[2]
The value of a particular rare stamp goes up by $5\%$ of its value at the start of each year. A collector paid $\$10\,000$ for the stamp at the beginning of 2005. Determine its value at the beginning of 2015, correct to the nearest $\$100$.
(b)[4]
For an arithmetic progression, the sum of the first $n$ terms is $\frac{1}{2} n(3n + 7)$. Determine the 1st term and the common difference of the progression.