Number Sequences and Shapes

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Number sequences and certain shapes are closely intertwined. Consider the number sequence

1, 3, 6, 10…

The nth term of this number sequence isWe can picture the number sequences as triangles made up of dots.

The nth triangle number is the number of dots in the nth triangle.

Similarly, consider the number sequence

1, 4, 9, 16…

The nth term of this sequence isWe can picture this number sequence as squares made up of dots.

The nth square number is the number of dots in the nth square.

Similarly, consider the number sequence

1, 5, 12, 22

The nth term of this sequence isWe can picture this number sequence as pentagons made up of dots.

The nth term of this sequences is the number of dots in the nth pentagon.

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