(a(i))[1]
Complete the table for the patterns in this sequence.
(a(ii))[2]
Find an expression, in terms of $n$, for how many counters are in Pattern $n$.
(a(iii))[2]
Jamal has $150$ counters. He uses them to make the largest possible pattern, Pattern $p$. Find the value of $p$.
(b(i))[2]
Find the initial term of this sequence.
(b(ii))[2]
Find an expression, in terms of $n$, for the $n$th term of this sequence.