Counting Problem: “How many dots in the n-th rectangle?”

Question

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1st rectangle

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2nd rectangle

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3rd rectangle

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4th rectangle

(please keep in mind the dots are closer together, but I didn’t know how to illustrate it on here, thanks)

The first (top) rectangle contains 2 dots. The 2nd rectangle contains 6 dots. The 3rd contains 12 dots. The 4th contains 20 dots.
How many dots in the 5th rectangle?
How many dots in the 100th rectangle? How do you know?
How many dots in the nth rectangle? How do you know?

Question

Note the Pattern:

1 st rectangle… 2 dots in 1 row
2 nd rectangle … 3 dots in 2 rows
3 rd rectangle … 4 dots in 3 rows
4 th rectangle … 5 dots in 4 rows

see the pattern?

nth rectangle … (n +1) dots in n rows.

Now how to count the dots? (n+1) dots in n rows give a total of n(n+1) dots for the nth rectangle.

For the 5th rectangle, it has 5*6 = 30 dots.
For 100th rectangle, it will have 100*101 or 10100 dots.