Question

The pentagonal numbers p1, p2, p3,....pk are the integers that count the number of dots in k nested pentagon, as shown in the figure ( in comment)
Show that p1 =1 and \(p_k =p_{k-1}+ (3k -2) \) for \(k\geq 2\). Conclude that \(\sum_{k=1}^n (3k -2)\) and evaluate this sum to find a simple formula for \(p_n\)
Please help