Answer:
Step-by-step explanation:
The worth of the card =$75
The value of the card decreases after each music purchase forming a sequence:
75,74.11,73.22,72.33...
Now,
- 74.11-75=-0.89
- 73.22-74.11=-0.89
- 72.33-73.22=-0.89
We see that the sequence forms an arithmetic sequence:
Where the first term, a is 75
Common difference, d=-0.89
We want to write an equation to define A(n), the amount of money on the gift card after n song purchases.
For an arithmetic sequence,the nth term A(n)=a+(n-1)d
Therefore:
The amount of money on the gift card after n song purchases.
A(n)=75-0.89(n-1)
A(n)=75+0.89-0.89n
A(n)=75.89-0.89n
To find out how many songs can Josh purchase with this card only, we take our nth term A(n) of the sequence to be 0 and solve for n.
A(n)=75.89-0.89n
0=75.89-0.89n
0.89n=75.89
Divide both sides by 0.89
n=85.3
n=85
Therefore, Josh can purchase 85 songs with this card only
