Math Investigations - IV
S&S Quiz #1
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Name:____________________________
1. For each sequence given below, mark which type(s) of sequence it could be:
a.
2 2 10 50
, , ,
5 3 9 27
b. 
1
1
1
1
,  ,  ,  ,,
10 10 10 10
c. 3, 4, 6,12,
d.
 Arithmetic
5 5 5 1
, , , ,
12 13 14 3
 Geometric
 Arithmetic
2 pts each
 Harmonic
 Geometric
 None of these
 Harmonic
 None of these
 Arithmetic
 Geometric
 Harmonic
 None of these
 Arithmetic
 Geometric
 Harmonic
 None of these
2. Given the following sequence is arithmetic, write an explicit formula for the sequence. 3 pts
a3  5 and a41  119  d 
119  5 114

 3 . Then a1  5  2  3  1
41  3
38
Explicit Formula:
an  1  3(n  1) or an  3n  4
3. If the following sequence is geometric, find the next two terms, then write explicit and
recursive formulas for the sequence. 5 pts
1
1 1
, , ________,
8 6
________ r 
6
1

4
3
8
Recursive Formula:
 1
 8 if n  1
an  
 4  a if n  1
 3 n 1
Explicit Formula:
1 4
an   
8 3
n 1
4. If the following sequence is harmonic, find the next two terms, then write an explicit formula
for the sequence.
4 pts
1 1
, , ________, ________
3 2
Associated arithmetic, bn , is: 3,  2,  7.......  bn  8  5n
Explicit Formula:
an 
1
8  5n
5. Write the terms of each of the following sequences. 2 pts each
5
 ( 1) n 1 
a. 

 n  1 n  2
1 1 1 1
 , , ,
3 4 5 6
 3 if n = 1

b. an n 1 where an   2 if n = 2
3a  a
 n 1 n  2 if n  2
6
3, 2, 3, 11, 36, 119
c.
 an  n  2
4
where an 
[0, 2], [1, 2],{2}
n
i 1
[i  2, 2i ] .