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Math 12 Pre-calculus Sept 6 – intro to sequences, including recursive sequences 1. For each, write out the number of required terms based on the conditions given a) the first 4 terms if tn = 3n – 2 b) the first 6 terms if tn = 2n – 1. What kind of numbers does this sequence make? c) the first 5 terms if tn = n(n + 2) d) the first 6 terms if tn = (tn-1)(tn-2) – 3 and t1 = 3, t2 = -2 e) the first 5 terms if tn = (n)(-1)n f) the first 10 terms if 2n , n is even tn 4 , n is odd g) the first 4 terms if tn = tn-1 + 6 and t1 = 7 2. Define the first term and then write a recursive formula for each a) b) c) d) 1,4,7,10,13…. 2, 6, 18, 54…. -3, 9, -27, 81… 3, 4, 9, 64, 3969… 3. The terms of the fibonacci sequence are 1,1,2,3,5,8,13…. Define these sequence recursively. 4. If a sequence is described by tn = 3tn-2 – 2tn-1, find the first term if t4 = 19 and t5 = -35 5. Do you remember what n! means? It is “factorial.” If you can’t remember what it means, you’ll need to look it up. Write out the first 6 terms if tn = n! 6. Consider the sequence described by tn 1 2 n1 a) Write out the first 6 terms b) Assume that n can become very large (very, very large)… a. Is this sequence increasing or decreasing? b. Is it converging or diverging? c. Is it bounded? 7. A recursive sequence is defined such that tn tn 1 . It is known that the fifth term is tn 2 1 12 Write out the first 6 terms. Is there anything you notice about this particular sequence? and the third term is 4.