Question 1:
A.) S = 2+4+6 = 12
B.) It is basically the same concept, you are adding things in a pattern.
C.) It makes logical sense because when you add something you'll get an answer relatively involving some qualities of the number.
Question 2:
A.) n=1, 1+2+3 = 6; n=2, 2+4+6 = 12; n=3, 3+6+9 = 18; n=4, 4+8 + 12 = 24; n=5, 5+10 = 15
B.) a divisor of n
C.) This does hold true for all n terms because that is the cool thing about numbers, they all have some relation to each other.
For question 1, when I say how does it compare to last week's, I don't mean how does the concept compare, I mean how do the sums themselves compare. Like when n=10, how are the sum of the first 10 positive even numbers and the sum of the first 10 positive integers related?
ReplyDeleteFor question 2, your sums aren't correct. You've produced the sums of the first three multiples of n... not 100% sure where that came from (and, in fact, n=5 doesn't even follow that pattern.)
Essentially you're just come up with the sequence
{a_n}= {6,12,18,24,15} Which really doesn't even follow a pattern.
Part B should be something far more clear-cut once you get the correct sums.
And finally, Part C needs to be much more in depth (as again, this is the point of the question for this week.) I'm asking you do actually take the time to think about everything put together and try to formulate some sort of justification for C. I really suggest reading over my comments for weeks 1 and 2.
Ciao.