CPSC170 Pre-lab 10
Recurrence relations

1. $1000 is initially deposited in a bank account that pays 8% annually. At the beginning of each subsequent year, an additional $100 is deposited into the account. So at the beginning of the first year the account holds $1000; at the beginning of the second year the account holds $100 + $1000 * 1.08 = $1180, and so on. If A(n) represents the amount of money in the account at the beginning of year n, write a recurrence relation for A. You do not have to find a closed-form solution; just write the recurrence relation.

   
   
   
   
   
   
   
   
   

2. Use the expand-guess-verify method to find a closed form solution for the sequence S:

   S(1) = 1
   S(n) = 1 + 3*S(n-1)
   

   Hint: 1 + 3 + 9 + ... + 3^n-1 = (3ⁿ-1)/2.