# File - math with mrs. Alligood

```PreCalculus Notes – 9.4 continued
RECURSIVE
EXPLICIT SEQUENCES:
RECURSIVE SEQUENCES:
Recursive sequences will give you the first term or so of the sequence. You will have to use the first term
to get the second…
Ex 1: Write the first 5 terms of the sequence a1 = 2; an+1 = 3 + an.
Notice that they already gave us the first term; a1 = 2. When finding terms in the sequence, we ALWAYS
start with n = 1 unless otherwise stated. So plug 1 into the equation, then n=2, and so on.
Solution:
Ex 2: find the first 5 terms of: a1 = 1, a2 = 2, an+2 = anan+1
Here, they have given us the first 2 already. Find the next 3 by plugging in 1, 2, 3 for n.
Solution:
Ex 3: Fibonacci Sequence: find the first 5 terms of: u1 = 1, u2 = 1, un+2 = un+un+1
Here, they have given us the first 2 already. Find the next 3 by plugging in 1, 2, 3 for n.
Solution:
Find the first four terms & the eighth term of the recursively defined sequence.
1. a1 = 8, an = an-1-4, for n≥2
2. u1 = -3, un+1 = un +10, for k≥1
3. b1 = 2, bk+1 = 3bk , for k≥1
4. v1 = 0.75, vn = (-2)vn-1 , for n≥2
5. c1 = -2, c2 = 3, ck = ck-2 +ck-1, for k≥3
Find a recursive rule for the nth term.
6. 6, 10, 14, 18, …
7. -4, 1, 6, 11, …
8. -5, -2, 1, 4, …
9. -7, 4, 15, 26, …
10.
The fifth and ninth terms of an arithmetic sequence are -5 and -17, respectively. Find a recursive
rule for the nth term.
```