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Trudy is starting a comic book collection. Let Cn represent the number of comic books that Trudy has after n weeks. The recursive relationship below represents Trudy's comic book collection.

C1 = 5
Cn + 1 = Cn + 2

Part A:
Write an explicit formula for Cn .

Part B:
Determine the number of comic books in Trudy's collection after 10 weeks. Explain how you determined your answer.

Respuesta :

Answer:

(A)

[tex]C_n=3+2n[/tex]

(B)

[tex]C_1_0=23[/tex]

Step-by-step explanation:

(A)

we are given

[tex]C_n_+_1=C_n+2[/tex]

[tex]C_1=5[/tex]

Firstly, we will find few terms

[tex]C_2=C_1+2[/tex]

[tex]C_2=5+2[/tex]

[tex]C_2=7[/tex]

[tex]C_3=C_2+2[/tex]

[tex]C_3=7+2[/tex]

[tex]C_3=9[/tex]

[tex]C_4=C_3+2[/tex]

[tex]C_4=9+2[/tex]

[tex]C_4=11[/tex]

so, we will get terms as

5, 7 , 9 , 11

we can see that this is arithematic sequence

First term =5

common difference =d=7-5=2

now, we can use nth term formula

[tex]C_n=C_1+(n-1)d[/tex]

now, we can plug values

[tex]C_n=5+2(n-1)[/tex]

[tex]C_n=5+2n-2[/tex]

[tex]C_n=3+2n[/tex]

(B)

we can plug n=10

[tex]C_1_0=3+2\times 10[/tex]

[tex]C_1_0=23[/tex]

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