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Manuel tore a piece of paper into three parts.He tore each part into three more parts.If Manuel repeated this action 12 times in total in total,how many pieces of paper would you have?

Sagot :

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;

  • After tearing the first piece of paper into 3 pieces. The number of pieces is 3.

  • The second time, each of the pieces was torn into 3 pieces each to yield; 3².

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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