The number of pieces of paper Manuel now has is ; 531441
Manuel tore the piece of paper into 3 parts each time.
In essence, the number of pieces of paper Manuel has will be given as;
3¹².
This is so because;
Ultimately, the number of pieces of paper is;
3¹² = 531441
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Manuel will have 531,441 pieces of paper if he repeats this action 12 times in total
This is a geometric progression exercise
Manuel tore the piece of paper into three parts. She has 3 pieces after the first time she carried out this action
This means that the first term of the sequence is a = 3
Manuel tore each of the three parts into three more parts. She will now have (3 x 3) pieces. That is, 9 pieces.
This means the second term of the sequence is 9
This is a geometric progression with a common ratio:
r = 9/3
r = 3
For the 12th action, n = 12
The number of pieces after the 12 action will be given as:
[tex]T_n = ar^{n-1}\\n = 12, a = 3, r = 3\\T_{12} = 3(3)^{12-1}\\T_{12} = 3(3)^{11}\\T_{12} = 3^{12}\\T_{12} = 531441[/tex]
Manuel will have 531,441 pieces of paper if he repeats this action 12 times in total
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