Problem Solving (PS) | What is the sum of the first 50 multiples of a positive integer K?

Zero is a multiple of every integer.

The first 50 multiples of\(K\) are
\(0K, 1K, 2K, 3K, . . . . 47K, 48K, 49K\)

Factor K out (we're interested in the arithmetic progression)

Sum of first 50 multiples of\(K\):
\(K(0 + 1 + 2 + 3 . . . + 47 + 48 + 49)\)

Sum of evenly spaced integers=
(Average)*(# of terms)

Average = \(\frac{FirstTerm+LastTerm}{2}\)
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