Download Objective 7.7: Recursive and Explicit Sequences Unit

Pre-Calculus Honors
Objective 7.7: Recursive and Explicit Sequences
Name_________________________________________
Ms. Hindal
Unit 7 Day 7
Brainstorm:
In words, explain the pattern in these sequences of numbers. Then, determine a) the next number in the sequence and b)
the 10th number in the sequence.
1) 5, 8, 11, 14…
2) 2, -2, 2, -2, 2…
3) 3, 3.1, 3.2, 3.3…
1 3 5 7
, , ,
4) 2 4 6 8 …
5) 0, 3, 8, 15, 24…
6) 1, 1, 2, 3, 5, 8, 13…

Sequences:
a1 :
a2 :
an :
Explicit Formulas:
Find the first three terms and the tenth term in the sequence:
1. an = 17 - 3n
2. an = 5(-1)n
 1n
2n
3.
an =
3.
a1 = 1 ; a2 = 4; an = an-1 – an-2
Recursive Formulas:
Find the next three terms of the sequence:
1. a1 = 1 and an = 4an-1
2.
a1 = 3 and an = 2 + an-1
Writing Sequences:
Recursive: In words, explain the pattern. Then write the recursive rule for the nth term:
1 1 1 1
 , , , ...
2 4 8 16
2.
1. ½, 7/8, 5/4, 13/8
3. 5, 15, 45, 135, …

Explicit: Write the sequence as an explicit formula:
1.
1 1 1 1
, , ,
3 9 27 81 , …
4.
1, 4, 9, 16, 25…
5.
1 2 3 4
, , , ...
2 3 4 5

2.
2, 6, 12, 20, 30…

3.
2, 4, 6, 8, 10…
Homework: Page 739, Section 9.4 Exercises – 1, 5, 7, 25 (c and d)
4 6 8
2, , , ,...
3 5 7
6. Challenge:
4.
Challenge:
1, 1, 2, 3, 5, 8, …
1.
Find an explicit and recursive formula for
-2, 4, -8, 16, -32…
2.
If a sequence is recursively defined as an = 4n -1 - 2n,
and a5 = 17, find the previous term. Then find a3.
3.
Karen recursively generated a sequence of five
positive integers by starting with a positive integer,
a1, and then applying the recursive formula an = an –
1 + 3n – 1 to generate an for n = 2, 3, 4, and 5. If the
value of a5 was 407, what was the value of Karen’s
starting term, a1 =?
A. 366
B. 367
C. 368
D. 369
4.
Is it easier to find recursive or explicit formulas in
your opinion? Always? Look back at examples from
your notes to try it out.
5.
A sequence is shown below:
2, 6, 12, 20, 30…
What is the recursive formula for this sequence?
A.
B.
C.
D.
tn = n + 2(tn – 1 + 1)
tn = (tn – 1 + 1)(n – 2)
tn = 2(tn – 1 + 2) – (n + 2)
tn = tn – 1 + 2(n + 1)
6.
Is the recursive formula or the explicit formula more
helpful for finding the next term? How about the 17th
term?
7.
If a sequence is defined by an = 3 + 4xn. Find the first
5 terms. Then find a recursive formula for the same
sequence.