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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 n1
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.