Question

A pattern is made by toothpick squares. Select the series that represents the number of toothpicks added to a picture to get the next picture to the right. Pretend the first picture has no toothpicks.
4 + 12 + 24 + 40 + ...; rule is an = 2(n2 + n)
1 + 2 + 3 + 4 + ...; rule is an = n
1 + 4 + 9 + 16 + ...; rule is an = n2
4 + 8 + 12 + 16 + ...; rule is an = 4n

The first one has one square the next one has 4 the next one has 9 and the last one has 16

Answer 1

The answer is, 4 + 8 + 12 + 16 ... rule is 4n.

Explanation:

one square has 4 toothpicks, then you added 4 picks (because you started with zero squares).

4 squares have 12 toothpicks, then you added 8 toothpicks to pass from one square to 4 squeres.

If you follow that reasoing you get to realize that the additions are 4, 8, 12, 16.