Give a recursive definition of the sequence {a_n}, n = 1, 2, 3, ... if a_n = 8n +3. a_n = (-3)^n. a_n = n^2 - l. a_n = (n+1)^2. Many garage doors have remote-access keypads outside the door. Let's suppose a thief approaches a particular garage and notices that four particular numbers are well-used. If we assume the code uses all four numbers exactly once, how many 4-digit codes does the thief has to try? Using the digits 1, 2, 3, 4 and 5, how many 5 digit numbers can be formed if the first digit must be 1 and repetition of the digits is allowed? The first digit must be 1 and repetition of the digits is not allowed? The number must be divisible by 2 and repetition is allowed? The number must be divisible by 2 and repetition is not allowed