The formula to represent the remaining value of the card is aₙ = 26.5 - 1.5n
The value of the card after ten downloads is $10
aₙ = a + (n - 1)d
where
a = first term
d = common difference
n = number of terms
Therefore,
a = 25
d = 23.5 - 25 = - 1.5
Therefore,
aₙ = 25 + (n - 1)(-1.5)
aₙ = 25 - 1.5n + 1.5
aₙ = 26.5 - 1.5n
After ten download the value of the card will be as follows,
26.5 - 1.5(11) = 26.5 - 16.5 = $10
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