Question 67449
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


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