Question

Please Help I am stuck! Write an explicit formula for the sequence and please explain. Thank you!

Answer 1

i can see why you are stuck! it doesn't look geometric or arithmetic
any ideas?

Answer 2

I have no idea! Sorry I stepped away from my computer for a second.

Answer 3

is this is some specific section of a book?
i don't see a relation between the numbers at all

Answer 4

hmmm, let me see....

Answer 5

No i'm afraid not. It's a very puzzling subject and I just can't seem to wrap my brain around it.

Answer 6

what is the topic in the book, if you are using one
maybe that would give a clue

Answer 7

I just looked it up: it's under "Identifying Mathematical Patterns".

Answer 8

damn, i thought i was decent at that....

Answer 9

I know, right? Exact thing went through my mind when I saw that question.

Answer 10

i do have kind of an idea

Answer 11

if we rewrite two of them it looks like this
\[\frac{2}{4},\frac{3}{7},\frac{4}{12},\frac{5}{19},\frac{6}{21}\]

Answer 12

yes, you're right.

Answer 13

well that doesn't help too much
numerators are clear, but denominators still a mystery
i thought maybe you were adding something to one to get to the next

Answer 14

oh i made a mistake!!

Answer 15

yeah, it seemed like that, it's just so weird. You helped out with the numerators though, that's very good!

Answer 16

\[\frac{2}{4},\frac{3}{7},\frac{4}{12},\frac{5}{19},\frac{6}{24}\]

Answer 17

almost looks like you add 5 each time, but not quite

Answer 18

ooh still a mistake! damn
now i see it

Answer 19

\[\frac{2}{4},\frac{3}{7},\frac{4}{12},\frac{5}{19},\frac{6}{28}\]

Answer 20

that's much better

Answer 21

Great, thank you. And these are just the numerators?

Answer 22

Sorry if that was an ignorant question, but I just wanted to ask.

Answer 23

no no i have both top and bottom, i just rewrote them to see a pattern

Answer 24

Okay, got it, thank you.

Answer 25

pattern in the numerator is clear
\[2,3,4,5,...\]

Answer 26

as for the denominator, i also see a pattern now
\[4,7,12,19,28,...\] do you see it? it is a bit harder

Answer 27

yes, I'm just starting to see it.

Answer 28

want me to tell you or would you like to figure it out?

Answer 29

Could you please explain it to me? Then I can take down the notes and then it will help me in the future.

Answer 30

first notice the differences in the denominator

Answer 31

\[7-4=3\\12-7=5\\19-12=7\\28-19=9\]

Answer 32

successive odd numbers
i happen to know that this will mean the formula is a quadratic
you can use
\(n^2+3\)
for \(n=1,2,3...\) and you will see that it works that way
if you don't know that, then you can still see that the differences are successive odd numbers, but if you do know it it will be a lot easier to compute \(a_{14}\)

Answer 33

great, you're right!

Answer 34

so \(a_{14}=\frac{14+1}{14^2+3}\) what ever that is

Answer 35

well actually i know what it is, it is
\[\frac{15}{197}\]

Answer 36

Sweet, is that all?

Answer 37

@satellite73 thank you, is that all? is it a b c or d?

Answer 38

? a b or c?

Answer 39

i have no idea

Answer 40

Sorry, I attached a photo of the problem at the top with my copier.

Answer 41

no solutions though, just the problem

Answer 42

i have to say, this was the best problem of the day!

Answer 43

Oy vey, that sound like me! let me re-do that. That's great, it was a very interesting problem, thank you for helping me out! Let me just check that picture though...

Answer 44

I speed typed out the answers.
A.
40, –53; an = (–1)n • (an – 1 + 2n – 1); explicit

B.

39, –50; an = (–1)n • (an – 1 + 2n – 1); explicit

C.

40, –53; an = (–1)n • (n2 + 4); recursive

D.

none of these

Answer 45

@satellite73

Answer 46

@satellite73