Question

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.

Answer 1

(A)

`C_n=3+2n`

(B)

`C_1_0=23`

Explanation:

(A)

we are given

`C_n_+_1=C_n+2`

`C_1=5`

Firstly, we will find few terms

`C_2=C_1+2`

`C_2=5+2`

`C_2=7`

`C_3=C_2+2`

`C_3=7+2`

`C_3=9`

`C_4=C_3+2`

`C_4=9+2`

`C_4=11`

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

`C_n=C_1+(n-1)d`

now, we can plug values

`C_n=5+2(n-1)`

`C_n=5+2n-2`

`C_n=3+2n`

(B)

we can plug n=10

`C_1_0=3+2* 10`

`C_1_0=23`