Question

Question #b3e6b

Answer 1

`103` toothpicks in the `50^"th"` figure.
`2n+3` toothpicks in the `n^"th"` figure.

Explanation:

In each progressive figure, one toothpick is added to the top row and one is added to the bottom row. As the `1^"st"` figure has `1` toothpick in the top row and `2` in the bottom row, that means that the `n^"th"` figure will have `n` toothpicks in the top row and `n+1` in the bottom row. Adding these to the `2` toothpicks which constitute the left and right sides, we get the total for the `n^"th"` figure as

`n + (n+1) + 2 = 2n + 3`.

To figure out how many are in the `50^"th"` figure, then, we just let `n=50` to get `2(50)+3 = 103`.