Write a recurrence relation and initial conditions for the number Sn of sequences of Nickles, dimes and quarters that can be inserted into a vending machine to purchase a soft drink costing 5n cents. How many sequences are there for a drink costing 50 cents?

For the infinite geometric sequence (xn) whose first four terms are:  1.3, 3.77, 10.933, 31.7057  find the values of the first term a and a common ratio r and write down a common recurrence system for this sequence.  Next, write down a closed form for this sequence and calculate the tenth term in this sequence to 3 dp

Select each expression that has a sum of 4 4/12 3 1/5 + 1 3/7 1 11/12 + 2 1/4 1 3/6 + 1 1/2 + 1 3/4 1 1/3 + 1 1/2 + 1 2/4 3/6 + 1 2/4 + 2 1/3

A four-bit code word is any sequence of four digits, where each digit is either a 0 or a 1. For example, 0100 and 1011 are four-bit code words. Complete parts (a) through (d) below. (a) How many different four-bit code words are there? 16 (b) How many different six-bit code words, such as 001011, are there? 64 (c) If a vocabulary of 1000 code words is required, how long must the words be? At least 10 bits. (d) What is the probability that a randomly selected four-bit code word has no 0 following any 1? |(Type an integer or a simplified fraction.)