Question

Grace loves to download new music. She originally had 47 songs but plans to purchase 3 new songs each week. She wants to know how many songs she will have after 104 weeks. Which equation should she use?

(A) a104 = 104 + 3(47 - 1)
(B) a104 = 104 + 3(47 + 1)
(C) a104 = 47 + 3(104 - 1)
(D) a104 = 47 + 3(104 + 1)

Answer 1

(C)
`a_1_0_4 = 47 + 3(104 - 1)`

Answer 2

Hence, the equation that represents the number of songs she will have after 104 weeks is:

`a_(104)=47+(104-1)* 3`

Explanation:

It is given that:

originally had 47 songs but plans to purchase 3 new songs each week. She wants to know how many songs she will have after 104 weeks.

Based on the data we see that:

Initial number of songs she has:

`a_1=47`

The number of songs she will have after second week is:

`a_2=47+3=47+3* (2-1)`

After Third week:

`a_3=47+3+3\\\\a_2=47+3* (3-1)`

and so on:

After 104 weeks she will have:

`a_(104)=47+(104-1)* 3`

Hence, option: C is the correct answer.

( This could also be seen as it form an arithmetic progression with initial term as a=47 and common difference i.e. d=3

Hence, the nth term is given by:

`a_n=a+(n-1)* d`

)