Justin has an I-tunes gift card worth $125. after he downloads his first app, the cards value is $118.01. after he downloads his second app, the cards value is $111.02. after he downloads his third app, the i-tunes gift card is worth $104.03. Justin wants to download as many apps as possible. what is the most number of apps Justin can download, using his i-tunes gift card

I have A(1)=118.01
A(2)=11.02
A(3)=104.03
each time I subtract $6.99

an=a1+(n-1)d
an=118.01+(14-1)-6.99
an=124.02

so a(14)=124.02
The most apps Justin can download is 14 apps.

Is this correct? thanks for checking my work and for any help.

3 answers

You get the idea, but there is something missing.
You have
A(0)=125
A(1)=118.01
A(2)=111.02
...
A(n)=125-6.99n
So when the card is used up, A(n)=0, or
125-6.99n=0
Solve for n=125/6.99=17.88
Drop the fraction to get 17 as the maximum number of apps he can download.

thank you for your help

You're welcome!