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Basic Mathematics Warmups

These problems and puzzles will put your deductive reasoning ability to the test and reinforce your mathematical skills.

Pyramid Counting Warmup

         

How many circles are in the final group?

Using the pattern above as an aid, evaluate the sum:

\[ 1 + 2 + 3 + 4 + 5 + 4 + 3 + 2 + 1 \]

Based on the previous question, evaluate:

\[ 1 + 2 + 3 + \dots + 8 + 9 + 8 + \dots + 3 + 2 + 1. \]

From what you have learnt, which expression represents the sum

\[ 1 + 2 + 3 + \dots + (n-1) + n + (n-1) + \dots + 3 + 2 + 1 ? \]

Hence or otherwise, what is the value of the expression:

\[ 1 + 2 + 3 + \dots + 49 + 50 + 49 + \dots + 3 + 2 + 1? \]

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