Question

Ryan is building a matchstick sequence as shown below. how many matches will he use for the Nth figure if the pattern of adding one new square horizontally and one vertically continues?

Answer 1

The first figure of the sequence uses 13 matches. To add a new square both horizontally and vertically, Ryan uses 6 additional matches. Therefore, the Nth figure will have 13 matches plus the sum of 6 at the Nth term.

The first figure will have 13 matches, the second 13+6=19, the third 13+6+6 and so on. To represent it, let's say S is the number of matches of the Nth figure.

To make it easier, we can say the term 0 will have 13 - 6 = 7 matches. Then:

$S=7+6N$