Pattern Solving Help

[Kraton9000]

First Off, this is my first time posting at these forums and I apologize if this is in the wrong category. I need immediate help in solving this one (apparantely simple) math problem that I simply cannot get a grasp on.

N = 1 2 3 4 5 6
F = 0 1 3 6 10 15

If N = 100
What is F?

Thanks in advance.

 

[stapel]

I need immediate help in solving this one (apparantely simple) math problem that I simply cannot get a grasp on.

N = 1 2 3 4 5 6
F = 0 1 3 6 10 15

If N = 100
What is F?

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

For instance, you looked at pairs of F-values, and noted that there is not a common difference, nor a common multiple:

. . . . .1 - 0 = 1, 3 - 1 = 2, 6 - 3 = 3, 10 - 6 = 4, and 15 - 10 = 5

. . . . .10*(3/2) = 15, 6*(5/2) = 10, 3*2 = 6, etc.

But did you notice anything in finding the above? Is there any possible pattern that you can use?

Please be complete. Thank you!

 

[Kraton9000]

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

For instance, you looked at pairs of F-values, and noted that there is not a common difference, nor a common multiple:

. . . . .1 - 0 = 1, 3 - 1 = 2, 6 - 3 = 3, 10 - 6 = 4, and 15 - 10 = 5

. . . . .10*(3/2) = 15, 6*(5/2) = 10, 3*2 = 6, etc.

But did you notice anything in finding the above? Is there any possible pattern that you can use?

Please be complete. Thank you!

Yes, I apologize for not doing so before. I have tried that problem and have determined that there is no common difference or common multiple.

However, I did notice that, excluding the first one, there seems to be a pattern in the number that one must add to N to get to F.

Here is a table:

1. F = N - 1
2. F = N - 1
3. F = N
4. F = N + 2
5. F = N + 5
6. F = N + 9

As you can see, aside from the first one, the number you have to add to N is always increasing by one. From step 2 to step 3, there is an increase of 1. From step 3 to step 4, there is an increase of 2. From step 4 to step 5, there is an increase of 3. From step 5 to step 6, there is an increase of 4.

I am not sure if I am on the right track, or lost in a completely different direction. But, regardless, I seem to be stuck and cannot comprehend what I have to do next. I hope my findings were specific enough. Thank you in advance.

 

[stapel]

Take a closer look at the differences:

1 - 0 = 1, 3 - 1 = 2, 6 - 3 = 3, 10 - 6 = 4, and 15 - 10 = 5

Do you see any pattern here?

n = 1: f(1) = 0
n = 2: f(2) = 1 = f(1) + 1
n = 3: f(3) = 3 = f(2) + 2
n = 4: f(4) = 6 = f(3) + 3
n = 5: f(5) = 10 = f(4) + 4
n = 6: f(6) = 15 = f(5) + 5

Is there any relationship between the n-values and what is being added?