2025 MI PU1 Promo Q4

The sum, \(S_n\), of the first \(n\) terms of a sequence \(T_1,\ T_2,\ T_3,\ldots\) is given by

1. Find a formula for \(T_n\) in simplified form.[2]
2. Show that the sequence \(T_1,\ T_2,\ T_3,\ldots\) is arithmetic and state the common difference.[3]
3. Find the sum of the \(10^{\text{th}}\) term to the \(20^{\text{th}}\) term.[2]