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QUESTION

# What is the sum of the first 10 positive integers?

55

The first 10 positive integers form an arithmetic sequence with initial term 1 and common difference 1.

The sum of a contiguous subsequence of an arithmetic sequence is the number of terms multiplied by the average of the first and last term.

In our case, there are 10 terms, with average value (1+10)/2 = 11/2.

So the sum of the sequence 1, 2, 3,..., 10 is:

10 * 11/2 = 55