Statement The kkk-th pentagonal number is Pk=k(3k−1)2P_k=\dfrac{k(3k-1)}{2}Pk=2k(3k−1). Compute P10P_{10}P10. Solution P10=10 (3⋅10−1)2=10⋅292=145.P_{10}=\frac{10\,(3\cdot 10-1)}{2}=\frac{10\cdot 29}{2}=\boxed{145}.P10=210(3⋅10−1)=210⋅29=145.