Question

To form 3 adjacent squares (as in the figure), 10 toothpicks are required. How many toothpicks are required to form 1000 adjacent squares?

Answer 1

3001

Explanation:

Let's say in general you want "n" adjacent squares. Each one needs a top, so that's n toothpicks. Each one needs a bottom, so that's another n toothpicks, and we're up to 2n total. You need one on the far left, and one on the far right, which brings us up to 2n + 2 toothpicks. Now we need to worry about the middle ones. But notice that you don't need n toothpicks for the interior because adjacent squares share. It turns out that you only need n-1. That brings us up to a grand total of 3n + 1 toothpicks, which would be 3001 for n = 1000.

Hope this helped!

Answer 2

Answer:Consider the given toothpick figures.

The perimeter of Figure 1 =

4

toothpicks.

The perimeter of Figure 2 =

10

toothpicks.

The perimeter of Figure 3 =

16

toothpicks.

Write a recursive formula for the perimeter of the nth figure.

an = an – 1 + 6 where a1 = 4

an = n2 where a1 = 1

an = an – 1 + 9 where a1 = 4

Explanation:

its 4, 10, 16

and then A

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