# Construct a graph based on the adjacency matrix and answer arithmetic sequence

**Question description**

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 II**

For 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.

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