Question

Write a possible explicit rule for the nth term: 1/2, 1/4, 1/6, 1/8, 1/10

Answer 1

Any help would be greatly appreciate! I have been stuck on this problem for about an hour. It's the last one and the most difficult! First differences are not constant, neither are the second differences or ratios. I'm confused as to how I'm supposed to tackle this problem.

Answer 2

If it were me, I would write the Prime Factorization of all the Denominators. This may lead to something obvious.

Answer 3

@tkhunny - Am I supposed to figure out the least common denominator between all of them?

Answer 4

Notice the denominators are all even.

Answer 5

a(n) = 1/(2n)

Answer 6

@tkhunny - 1/2: 2 x 1 , 1/4: 2 x 2 , 1/6,: 3 x 2, 1/8: 4 x 2; 2 x 2 x 2, 1/10: 5 x 2
I do see a pattern here! :)

Answer 7

@myininaya thanks for the hint!
@sourwing - may I ask how you got that answer?

Answer 8

well, 2 = 2*1
4 = 3*2
6 = 2*n
...
so 1/(2n)

there's not much else I can say except the pattern is obvious

Answer 9

2*1
2*2
2*3
2*4
2*5
Are you SURE you don't see a pattern?

Answer 10

@sourwing - that's what I thought. I was just making sure. :p
@tkhunny - Yes, I do see a pattern. I already said that I did!

Answer 11

Thanks for the help guys! I really appreciate it. :)

Answer 12

eheheh

Answer 13

My b. Didn't read the whole thread. :-)

Answer 14

the file is not relevant btw =)

Answer 15

just putting up a file for a quick link, is all =)

Answer 16

@jdoe0001 - I suggest using imgur for that. I don't want you to get in trouble for posting irrelevant information on an already closed question!

Answer 17

indeed