Question

Samantha loves to download new music. She originally had 52 songs but plans to purchase 2 new songs each week. She wants to know how many songs she will have after 93 weeks. Which equation should she use?

a93 = 93 + 2(52 − 1)
a93 = 93 + 2(52 + 1)
a93 = 52 + 2(93 + 1)
a93 = 52 + 2(93 − 1)

Hint: It's either A, B, C, or D

Answer 1

They want to construct this in the form of an arithmetic sequence which as the form:

a(n)=a+d(n-1), where a=initial value, d=common difference.

In this case a=52 and d=2, so our formula is:

a(n)=52+2(n-1) and if we are looking for the 93 term we have

a(93)=52+2(93-1)

Answer 2

`a_1=52\\ d=2\\ n=93\\\\ a_n=a_1+(n-1)\cdot d\\\\ a_(93)=52+(93-1)\cdot2=52+2(93-1)`