Find the nth term of the sequence -2,6,14,22...
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Answer:
6*8=48 groups with elements of order 7
Step-by-step explanation:
For this case the first step is discompose the number 168 in factors like this:
And for this case we can use the Sylow theorems, given by:
Let G a group of order where p is a prime number, with
and p not divide m then:
1)
2) All sylow p subgroups are conjugate in G
3) Any p subgroup of G is contained in a Sylow p subgroup
4) n(G) =1 mod p
Using these theorems we can see that 7 = 1 (mod7)
By the theorem we can't have on one Sylow 7 subgroup so then we need to have 8 of them.
Every each 2 subgroups intersect in a subgroup with a order that divides 7. And analyzing the intersection we can see that we can have 6 of these subgroups.
So then based on the information we can have 6*8=48 groups with elements of order 7 in G of size 168
i = (100m)/c
lowest i = 80, highest i = 120
c = 12
this will result in 2 equations, one will be the lowest (solving m when i = 80), and the highest (solving m when i = 120)
solve m when i = 80:
i = (100m)/c
80 = (100m)/12
80×12 = 100m
960 = 100m
960/100 = m
9.6 = m
solve m when i = 120:
i = (100m)/c
120 = (100m)/12
120×12 = 100m
1440 = 100m
1440/100 = m
14.4 = m
therefore,