Heather's #3

Question 1:

A) n=1: 2=2
n=2: 2+4=6
n=3: 2+4+6=12
n=4: 2+4+6+8=20
n=5: 2+4+6+8+10=30
n=6: 2+4+6+8+10+12=42
n=7: 2+4+6+8+10+12+14=56
n=8: 2+4+6+8+10+12+14+16=72
n=9: 2+4+6+8+10+12+14+16+18=90
n=10: 2+4+6+8+10+12+14+16+18+20=110

B) Okay, so looking back at last week's sums I saw they were, starting at n=1,:
1, 3, 6, 10, 15..With those numbers, I noticed that to get the next sum number, all you have to do is add the next "n"..meaning that if I wanted to find the sum number after 6, where n=3, all I would have to do is add the next "n" which would be 4. And that would give me the correct sum, 10. Now for this week, since the numbers are only even numbers, there's a bigger jump from one sum number to the next. First looking at only the sum #'s, I saw that starting with 2 you add 4, then you add 4, then 6, then 8, etc. to get the next sum number..Soooo, I figured you must have to multiply something together in order to get the formula. The simple formula I came up with to find the sums is 2n. now I say "simple" because that isn't the actual formula, it just sort of gets you where you need to be. Using the formula I had last week, I made a minor adjustment for it to work this time. So my formula for this is 2n(n+1)/2 ..where all you have to do to find the sum is plug in n.

C) Well I'd say it makes logical sense because it's basically the same concept as what we did last week, just with a different category of numbers..So therefore, you would have to tweek the formula a little bit in order for it to work properly.

Question 2:

A) n=1: 1=1
n=2: 1+3=4
n=3: 1+3+5=9
n=4: 1+3+5+7=16
n=5: 1+3+5+7+9=25
n=6: 1+3+5+7+9+11=36
n=7: 1+3+5+7+9+11+13=49
n=8: 1+3+5+7+9+11+13+15=64

B) Obviously looking at the sums, the formula for this would simply be n^2 because all the sums are in fact, perfect squares.

C) This holds true for all n because no matter what n is, you're going to multiply it by itself to get your sum every time. So therefore that will not change anything. And there are really no specifics when it comes to the "category" of the number..(as in if it's even, odd, a palindrome, etc.) So for example if you are asked to find the sum when n=137, all you do is multiply 137 by itself and you get 18769.