Problem 4 (8 points): A Silicon Valley billionaire purchases 3 new cars for his

Question

Problem 4 (8 points): A Silicon Valley billionaire purchases 3 new cars for his collection at the end of every month. Let an  denote the number of cars he has after n months. Let a0 = 23

- What is a8

- If he pays $50 each month to have a car maintained, how much does he pay for maintenance after 2 years? No need to calculate the actual number. Instead give a closed form (without the summation) mathematical expression for the number. Note that he purchases the new car at the end of each month, so during the first month, he is only maintaining 23 cars.

Explanation / Answer

a)

a_0 = 23

a_8 => 8*3 + a_0 => 24 + 23 => 47

a_8 = 47

b)

a_0 = 23

a_1 = 3 + 23

.

.

a_24 = (24*3 + 23) * 50

a_n = (n*3 + 23) * 50 -> for nth month

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