The first four terms of a sequence are \(T_1=1\times3=3\), \(T_2=1\times3+3\times3=12\), \(T_3=1\times3+3\times3+5\times3=27\), and \(T_4=1\times3+3\times3+5\times3+7\times3=48\).
Find an expression, in terms of \(n\), for \(T_n\).[1]
\(T_p\) and \(T_{p+1}\) are consecutive terms. Find and simplify an expression, in terms of \(p\), for \(T_{p+1}-T_p\).[1]
Explain why two consecutive terms cannot have a difference of 4.[1]
The first three terms of a second sequence are 12, 27 and 48. Using (a) or otherwise, write down an expression, in terms of \(n\), for its \(n\)th term \(S_n\).[1]