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

Answer:

(A)

$C_n=3+2n$

(B)

$C_1_0=23$

Step-by-step 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

$C_1_0=3+2\times 10$

$C_1_0=23$