Ask Question
13 November, 09:44

Josh has a itunes gift card worth $75. After he purchases the first song on itunes, the cards value is $74.11. After he purchases the second song, its value is $73.22. After he purchases the third song, its value is $72.33. Assuming the pattern continues, write an equation to define A (n), the amount of money on the gift card after n song purchases.

How many songs can Josh purchase with this card only?

+5
Answers (1)
  1. 13 November, 11:16
    0
    A (n) = 75.89-0.89n 85 songs

    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
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Josh has a itunes gift card worth $75. After he purchases the first song on itunes, the cards value is $74.11. After he purchases the ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers