2010 AJC P1 Q11

Part of an isosceles triangle, formed by numbers following a particular pattern is shown below:

1. State the middle term in the \(n^{\mathrm{th}}\) row.[1]
2. Find the first and last term of the \(n^{\mathrm{th}}\) row.[2]
3. Show that the sum of the terms in the \(n^{\mathrm{th}}\) row is \(\left( 2n-1 \right){{3}^{n-1}}\).[2]
4. Find the minimum number of rows in the triangle for the number of terms in the triangle to exceed \(500\).[3]