Question

Medal and Fan! Please help! :)
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

What do you think the answer is?

Answer 2

A ?

Answer 3

why?

Answer 4

I don't really know. I do not understand.

Answer 5

its either c or d

Answer 6

Would I figure out how many songs she would have and then solve each equation to see if it matched? Or would that not work?

Answer 7

I would solve the problem and look back to see which other equations worked that should be your answer.

Answer 8

Yes, that is what I meant :) I will try that and see.

Answer 9

Okay so the number of songs she has can be expressed as an arithmetic sequence where the first term is 47 and the common difference is 3. The formula for that is:\[a_n=a_1+(n-1)d\]Where d is the common difference: 3. n is the nth term (ie number of weeks in this scenario) and a1 is the first term: 47. Putting in our values we get:\[a_n= 47 + (n-1)*3\]So if we want to find the term when n=104 (104 weeks later), we simply sub n=104 into this:\[a_{104}=47+(104-1)*3\]
Which answer is this equal to?

Answer 10

tom you wouldn't have to do that.

Answer 11

In this case you could just find the answer and go through the formula to see if its correct.

Answer 12

So the answer would be C?

Answer 13

Correct.

Answer 14

Thank you guys! :)

Answer 15

Medal?

Answer 16

Thanks :)

Answer 17

@Andrewthehelper, this is clearly a sequences question so I don't know why you're suggesting to solve it any other way. Sure there are other ways, but this is the right way to do it.

Answer 18

@sunmidge, no problem. Hope you understand it a bit better now!

Answer 19

Tom I know, its just an easier way to solve.

Answer 20

its just a lil trick

Answer 21

I do. Thank you for the help @tom982 :)

Answer 22

@Andrewthehelper, sure shortcuts are nice but you need to understanding how to do a question properly before using any. If you don't, you could end up facing a question requiring this knowledge applied another way and you wouldn't have a clue what to do.

Answer 23

Correct