Recurrence relations

- $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.

- 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}= (3^{n}-1)/2.