Math Investigations - IV
Quiz #1
Show all work.
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


5. Write out the terms of the sequence an n 1 where an  
2 if n = 2
2a  3a
n  2 if n  2
 n 1
4
n
1
6. Given the explicit formula for the arithmetic sequence: an  3    . Write a
2
recursive formula an for using the correct format.
 3 if n = 1
7. Given the recursive formula: an  
. Write an explicit formula an .
an1  5 if n  1
Writing out the first few terms: 3, 2, 7, 12,...... , we recognize this as an arithmetic
sequence with a1  3, and d  5 . (Could we have recognized this without writing out
the terms? – Hint: yes).
Then,
an  3  5(n  1)
 8  5n
 1
 7 if n = 1

8. Given the recursive formula: an   1
. Write an explicit formula an .
if
n

1
 1
4

 an 1
As in 7, writing out the first few terms:
1 1 1 1
, , , ,......
7 11 15 19
Could it possibly be harmonic? Yes, since the sequence 7,11,15,19….. is arithmetic.
Then the associated arithmetic is given by bn  3  4n .
1
So, an 
3  4n