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Jonah stacks balls of yarn in a square pyramid for a store display. The number of balls of yarn, P(n), in "n" layers of a square pyramid is given by
P(n)=P(n-1)=n^2 what number could not be the number of balls Jonah stacks.

A.14
B.24
C.5
D.30

Respuesta :

WojtekR
[tex]P(1) = 1\\\\P(2)=P(1)+2^2=1+2^2=1+4=5\\\\P(3)=P(2)+3^2=5+3^2=5+9=14\\\\P(4)=P(3)+4^2=14+4^2=14+16=30[/tex]

Correct answer is B. 24

The number of ball which Jonah could not stacks are [tex]24[/tex] given in option [tex](B)[/tex].

What is Pyramid ?

Pyramid is a shape or structure with a polygon for its base and three or more triangles for its sides which meet to form the top

We have,

The number of balls of yarn [tex]= P(n)[/tex]

"[tex]n[/tex]" Number of layers of squared pyramid are given as;

[tex]P(n)=P(n-1)+n^2[/tex]

So,

Let number of layers  [tex](n) = 1[/tex] ,

Then,

[tex]P(1) = P(1-1)+1^2=1[/tex]

        [tex]= P(0)+1=1[/tex]

Now,  [tex](n) = 2[/tex] ,

[tex]P(2) = P(2-1)+2^2[/tex]

        [tex]= P(1)+2^2=1+4[/tex]

[tex]P(2) = 5[/tex]

Now,  [tex](n) = 3[/tex] ,

[tex]P(3) = P(3-1)+3^2[/tex]

        [tex]= P(2)+9=5+9[/tex]

[tex]P(3) = 14[/tex]

Now,  [tex](n) = 4[/tex] ,

[tex]P(4) = P(4-1)+4^2[/tex]

        [tex]= P(3)+16=14+16[/tex]

[tex]P(4) = 30[/tex]

Now,  [tex](n) = 5[/tex] ,

[tex]P(5) = P(5-1)+5^2[/tex]

        [tex]= P(4)+25=30+25[/tex]

[tex]P(5) = 55[/tex]

So, from the value we can see that [tex]24[/tex] is that number which could not be stacked.

Hence, we can say that the number of ball which Jonah could not stacks are [tex]24[/tex] given in option [tex](B)[/tex].

To know more about pyramid click here

brainly.com/question/18073768

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