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)

Answer 1

This is an arithmetic progression: 52, 54, 56, 58, 60 ....

difference, d = 2

First term, A1 = 52

Last term, A93: 52 + 2(93 -1).
But this is the last download, the number of songs that she will have (if she keeps all of the songs that she downloaded) is given by the sum of the terms.

The sum is given by the formula, S = [A1+An]*n/2 = [52 + 52 + 2(93-1)]*93/2 =

= [52 + 92]*93

The option D in the list of choices represent the number of songs that she will download in the week 93 (not the number of songs that she will have, because for that you have to sum 52 + 54 + 56 +... + [52*2*(93-1)]