# I think I found an unlisted alternate solution to one of the course problems

I am on the Algebra with puzzles course; Pentagonal and Hexagonal numbers, and on question 2. I will write it out so you won't have to go see it for yourself. The pentagonal numbers are the sequence: 1, 5, 12, 22, 35 etc... What is the difference between the 99th pentagonal number and the 100th? The answer to the question is exactly stated as follows; "In order to find the difference between the 99th and 100th pentagonal numbers, we use the fact that the difference will have increased by three 98 times, plus the original 4 that it increased between the first and second values: 98 (3) + 4 = 298" However, I came to this conclusion: Since we are asked to find the increments of change and we know that the number that is being added keeps on being increased by 3, we can determine that the 99th difference is 99 x 3. That leaves us with 297, 1 away from the answer of 298, then we add 1 because we started out pattern with the number 1 leaving us with our answer of 298.

On a final note, I was curious if users on this platform take any notes when it comes to learning material from the provided courses in the premium version or even from the community posted questions. I do this and I found it very helpful but as I find that the questions become more and more complex and long I end up using more time writing down the answers than I do working on the questions themselves.

Note by Reno Jackson
3 months, 4 weeks ago

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