Math Investigations - IV
Sample Quiz
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Name:____________________________
1. If the following sequence is arithmetic, find the next two terms, then write an explicit
formula for the sequence.
3,  2, ________,
________
Explicit Formula:
2. If the following sequence is geometric, find the next two terms, then write an explicit
formula for the sequence.
2 2
, , ________,
5 3
________
Explicit Formula:
3. If the following sequence is harmonic, find the next two terms, then write an explicit
formula for the sequence.
1 1
, , ________,
3 2
________
Explicit Formula:
4. Dr. Price and Dr. Fogel write all the MI-4 problem sets. Because Dr. Fogel likes to
write long-winded word problems it takes him 50 minutes to write a problem set
while Dr. Prince can write one in only 30 minutes. Assuming that they write at a
uniform rate, how long will it take for them to write a problem set if they work on it
together, both working until the problem set is finished?
3 if n = 1


2 if n = 2
5. Write out the terms of the sequence an n 1 where an  
2a  3a
n  2 if n  2
 n 1
4
n
1
6. Given the explicit formula: an  3    . Write a recursive formula an for using the
2
correct format.
 3 if n = 1
7. Given the recursive formula: an  
. Write an explicit formula for an .
an1  5 if n  1
 1
 7 if n = 1

8. Given the recursive formula: an   1
. Write an explicit formula for an .
if n  1
 1
4

a
 n 1