Sequential pattern mining is very important because it is the basis of many applications. Although there has been a great deal of effort on sequential pattern mining in recent years, its performance is still far from satisfactory because of two main challenges: large search spaces and the ineffectiveness in handling dense datasets. To offer a solution to the above challenges, we have proposed a series of novel algorithms, called the LAst Position INduction (LAPIN) sequential pattern mining, which is based on the simple idea that the last position of an item, α, is the key to judging whether or not a frequent k-length sequential pattern can be extended to be a frequent (k+1)-length pattern by appending the item α to it. LAPIN can largely reduce the search space during the mining process, and is very effective in mining dense datasets. Our performance study demonstrates that LAPIN outperforms PrefixSpan [4] by up to an order of magnitude on long pattern dense datasets.