Question

in the sequence of non-zero numbers x, x^2, x^3, x^4, ..., .if from the third term on, each term is the sum of the preceding 2 terms, what are all the possible values of x

Answer 1

I'm guess those superscripts are definitely not exponents?

Answer 2

its x raised to 1,2,3,4... sory I don't know how to sophistically type them on my pc keyboard :)

Answer 3

so they are exponents

Answer 4

\[x,x^2,x^3,x^4,x^5,...\]

Answer 5

but if that is so then this is also a geometric series

Answer 6

but anyways you are given that \[x^3+x^4=x^5\]
or ...
\[x^{n-2}+x^{n-1}=x^{n} \text{ for } n \ge 5\]

Answer 7

i found n >or = 3 but 5 makes sense

Answer 8

well it said for the third term and on...

Answer 9

so it sounded like x^1+x^2 doesn't imply the third term is x^3

Answer 10

wait maybe it does mean that

Answer 11

maybe you are right

Answer 12

\[x^{n-2}+x^{n-1}=x^{n} \text{ for } n \ge 3 \]

Answer 13

that'
s what i have so far

Answer 14

but if we just look at the first case n=3
\[x+x^2=x^3 \]
we should be able to solve this equation for x

Answer 15

we already know x is not 0
so divide both sides by x
and you have a quadratic to solve

Answer 16

omg! so 1+x=x^2.... yeah that makes sense! thanks!

Answer 17

you don't get pretty values

Answer 18

quadratic formula! ^_^ hehe its fine for me

Answer 19

have fun

Answer 20

thanks!