What is the general term equation, a_n , for the arithmetic sequence 5, 1,–3, –7…and what is the 21st term of this sequence? hint: a_n=a_1+d(n-1), where a_1 is the first term and d is the common difference

Suppose the first five terms of a sequence are 4, 5, 9, 27, 123. how could the next term in the sequence be generated?

How much dextrose 70% must be mixed with dextrose 5% to prepare 1,000 ml of dextrose 20%?

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries. (a) if he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) if 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (round your answer to three decimal places.) (e) if 6 bottles are randomly selected, what is the probability that all of them are the same variety? (round your answer to three decimal places.)