How do you find m when mZZ=<-10,8,26> ? (Abstract algebra)

when mZZ=<-10,8,26>

1 Answer
Oct 17, 2017

m=color(red)(18)

Explanation:

If mZZ = <...,-10,8,26,...>
color(white)("XXXXXXXXXX")Note
color(white)("XXXXXXXXXXXX")I assumed you meant the ordered set to be infinite
color(white)("XXXXXXXXXXXX")and not limited to only 3 elements
then EEk | k in ZZ
and < m * (k-1), m * k, m *(k+1 )> = < -10,8,26 >

[1]color(white)("XXX")mk-m=-10
[2]color(white)("XXX")mk=8
[3]color(white)("XXX")mk+m=26

If we subtract [2] from [3], we get
[4]color(white)("XXX")m=16

We can verify this result by substituting 8 for mk and 16 for m in [1] and getting the required result: -10