SOLUTION: 5. each number trick below is generated by the same number trick. First sequence: 3, -1, -3, -12, -4, 3 Second sequence: 10, 6, 18, 9, 3, 10 Third sequence:

Algebra ->  Algebra  -> Signed-numbers -> SOLUTION: 5. each number trick below is generated by the same number trick. First sequence: 3, -1, -3, -12, -4, 3 Second sequence: 10, 6, 18, 9, 3, 10 Third sequence:      Log On

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Question 67449This question is from textbook
: 5. each number trick below is generated by the same number trick.
First sequence: 3, -1, -3, -12, -4, 3
Second sequence: 10, 6, 18, 9, 3, 10
Third sequence: 5, …
A. describe this number trick in words
B. complete the third sentence
C. write a sequence of expressions for this number trickThis question is from textbook

Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
The sequence is interpreted as----subtract 4, multiply by 3, subtract 9, divide by 3, add 7.

CHECK:
for the first sequence,
Starts with 3
3-4=-1_____________________________________subtract 4
-1*3=-3____________________________________multiply by 3
-3-9=-12___________________________________subtract 9
-12/3=-4___________________________________divide by 3
-4+7=3_____________________________________add 7
The highlighted numbers form the sequence 3, -1, -3, -12, -4, 3

For the second sequence
starts with 10
10-4=6___________________________________________subtract 4
6*3=18___________________________________________multiply by 3
18-9=9___________________________________________subtract 9
9/3=3____________________________________________divide by 3
3+7=10___________________________________________add 7
The highlighted number reveal:10,6,18,9,3,10

THus, the pattern I made is correct. Applying this to the THIRD sequence,
starts with 5
5-4=1____________________________________________subtract 4
1*3=3____________________________________________multiply by 3
3-9=-6___________________________________________subtract 9
-6/3=-2__________________________________________divide by 3
-2+7=5___________________________________________add 7


The highlighted numbers reveal the sequence: 5,1,3,-6,-2,5

Ok, I'll make my own. I'll start with 8.

starts with 8
8-4=4__________________________________________subtract 4
4*3=12_________________________________________multiply by 3
12-9=3_________________________________________subtract 9
3/3=1__________________________________________divide by 3
1+7=8__________________________________________add 7

Notice that the first and last terms are always the same.
It can be proved algebraically
If x is the first term,
starts with x
x-4=x-4________________________________________subtract 4
(x-4)*3=3x-4*3=3x-12___________________________multiply by 3
(3x-12)-9=3x-21________________________________subtract 9
(3x-21)/3=(3x/3)-(21/3)=x-7____________________divide by 3
(x-7)+7=x+0=x__________________________________add 7
The highlighted terms form : x, x-4, 3x-12, 3x-21, x-7, x
The first term is x and the last term is x

Power up,
HyperBrain!