Answer:
Hence, the equation that represents the number of songs she will have after 104 weeks is:
\(a_{104}=47+(104-1)\times 3\)
Step-by-step 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:
\(a_2=47+3=47+3\times (2-1)\)
After Third week:
\(a_3=47+3+3\\\\a_2=47+3\times (3-1)\)
and so on:
After 104 weeks she will have:
\(a_{104}=47+(104-1)\times 3\)
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:
\(a_n=a+(n-1)\times d\)
)
