In how many ways can 345 be written as the sum of an increasing sequen

I couldn't recognize the pattern quick enough.....taking 5 minutes, definitely can answer the Question.

2 Consecutive Integers is easy: X + (X + 1)
2X + 1 = 345
2X = 344

Since 344 is Even, then yes, 345 can be written as 2 Consecutive Integers


Then for Each Additional Consecutive Integer you test

1st)you make the Co-Efficient in front of X = (No. of Consec. Integers) * X

2nd) keeping adding an additional (X +1 to the Prior Term)

The Pattern will go like this

2 Consecutive Int. = 2x + 1 (1/2 of the Co-Efficient)

3 Consecutive Int. = 3x + 3 (1 Extra Number = Co-Efficient Added)

4 Consecutive Int. = 4x + 4 + 2 (1 Extra Number = Co-Efficient Added + 1/2 a Coefficient)

5 Consecutive Integers = 5x + 5 + 5 (2 Extra Numbers = Co-Efficient Added)

6 Consecutive Integers = 6X + 6 + 6 + 3 (2 Extra Numbers = Co-Efficient Added + 1/2 a Coefficient)

7 Consecutive Integers = 7X + 7 + 7 + 7 (3 Extra Numbers = Co-Efficient Added)

8 Consecutive Integers = 8X + 8 + 8 + 8 + 4 (3 Extra Numbers = Co-Efficient Added + 1/2 a Coefficient)


and the pattern will continue

I found 2 , 3 , 5 , 6 , 10 , and 15 consecutive integers worked. Then I saw the time lol


EDIT: the Post Above mine seems like a much more efficient use of time.