I have to write two papers with a supporting document about math

Construct a graph based on the adjacency matrix that appears below. Label all nodes with indices consistent with the placement of numbers within the matrix.Then, answer the questions that follow.| 0 3 6 8 5 2 || 3 0 4 9 0 0 || 6 4 0 4 0 0 || 8 9 4 0 2 0 || 5 0 0 2 0 0 || 2 0 0 0 0 0 |How many simple paths are there from vertex 1 to vertex 4?Which is the shortest of those paths? How did you determine that?Part IIFor the following arithmetic sequence {3, 9, 15, 21, 27, .}, answer the following questions:Clearly state the equation used to describe this sequence.Determine the 6th, 22nd, and the 89th elements.Clearly state the equation used to sum the 22nd element through the 89th element.Calculate the sum of the first 89th elements.