Originally Posted by

**anthmoo** That's the best title i could do that's descriptive...

Here is the algorithm..

Step 1: Input a positive integer *n*

Step 2: Draw a graph consisting of n vertices and no arcs.

Step 3: Create a new vertex and join it directly to every vertex of order 0.

Step 4: Create a new vertex and join it directly to every vertex of **odd** order.

Step 5: Stop.

I put in the integers 1 to 5 in the algorithm and got the results of the number of arcs as...

n=1, a=3

n=2, a=4

n=3, a=7

n=4, a=8

n=5, a=11

The question asks:

State how many arcs are in the graphs that results when the algorithm is applied to a set of n vertices.

So basically the question is asking what is the nth term of these numbers:

3, 4, 7, 8, 11

Please could someone help me understand the method of how they got the nth term?

Thanks guys!