Question #b3e6b

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Question #b3e6b

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Answer 1 · 2016-09-14T06:55:16

$103$ $103$ toothpicks in the $50^{th}$ $50^"th"$ figure.
$2 n + 3$ $2n+3$ toothpicks in the $n^{th}$ $n^"th"$ figure.

Explanation:

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

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

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

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