How many terms will have their sum as 72 in the following series 17, 15, 13, ________?

The series is an arithmetic progression with the first term 17 and a common difference of -2. The sum formula for an arithmetic progression is S = n/2 times (2a + (n - 1)d). Substituting the known values gives 72 = n/2 times (34 + (n - 1)(-2)), which simplifies to 72 = n(18 - n). Solving the quadratic equation n^2 - 18n + 72 = 0 gives n = 6 or n = 12. The sequence becomes negative after nine terms, so the correct count is 6 terms.

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