Question

Given the explicit formula u(n) = 5^n-1, where u(1) = 1, find the recursive formula for u(n).

Answer 1

what did you do so far?

Answer 2

any ideas

Answer 3

nothing. I have no idea how to do this

Answer 4

how about finding u2 u3 and see what is going on here

Answer 5

can you do u2

Answer 6

I don't know how t do it

Answer 7

we have the explicit formula
\(\huge u_n=5^n-1\)

Answer 8

so\(\huge u_2=5^2-1\) yess?

Answer 9

just replacing n with 2

Answer 10

so \(\huge u_2=24\)

Answer 11

let's see if yu can do \(\huge u_3\)

Answer 12

Did you look at the attached file?

Answer 13

i don't really care about the attached file

Answer 14

that's just to check for the last thing to do

Answer 15

what you need to focus on is finding the formula
from those terms

Answer 16

I see what you're saying and i'm kind of getting it but it's not matching the answers

Answer 17

it doesn't matter for now okay

Answer 18

to find the general formula you have to derive by doing what are doing now

Answer 19

okay so i need to figure out what u3 means right?

Answer 20

yes!

Answer 21

I'm so sorry but my session timed out and took me to a new question. I think i get it though.

Answer 22

by this point you should see the pattern

Answer 23

oh does not matter, what matters is you understand what you are doing
not the homework or quiz itself

Answer 24

oh hold i miss typed it...
correction in the next reply

Answer 25

i just realize i was doing a wrong problem
it should be \(\huge u_n=5^{n-1}\) not \(\huge u_n=5^n-1\)you should correct me
on this from the beginning

Answer 26

i was dealing with something different

Answer 27

but we still have \(\huge u_2=5\\ \huge u_3=5^2 \\ \huge u_4=u^3\)
so apparently \(\huge u_3=5^2=5*5=5u_2\)
and \(\huge u_4=5*5^2=5u_3\) and you can check \(\huge u_5, u_6\) if you want
we generalize from this that \(\huge u_{n+1=5\huge{u_n}}\)

Answer 28

if you check you answer that you have you get the third one

Answer 29

the first one i mean D

Answer 30

do you get it?

Answer 31

just look at the pattern

Answer 32

sorry about the confusion i went a wrong equation in the beginning

Answer 33

so the one you are looking for is
\(\huge u_{n+1}=5u_n\)

Answer 34

that's the recursive formula

Answer 35

any further help?