Question 1044272: All terms of an arithmetic sequence are integers. The first term is 535, the last
term is 567, and the sequence has n terms. What is the sum of all possible values
of n?
Answer: 69 (How)?
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! OK.
So take the sequence that has a starting value of 535 and a last value of 567 which would be a difference of 32.
That sequence has two values: 535, 567
.
.
On the other end, take the one that has a difference of 1.
535,536,537,...,566,567.
That one has 33 values.
So then so far you have,
Keep going this way and look for all sequences.
You know the differences are limited to values between 1 and 32 and they must be integers.
You'll quickly notice a certain pattern which should lead you to your answer.
Using EXCEL may be able to speed up the process.
Good luck and repost if you need more help.
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