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:
 Arithmetic
a. 1, 2, 6, 24,
b. 
1 1 1 7 1
, , , , ,
10 20 5 20 2
 Arithmetic
c. 3, 4, 6,12,
d.
5
5 5 10
, , , ,
12 6 3
3
 Geometric
 Geometric
 Harmonic
 Harmonic
 None of these
 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.
a3  65 and a11  25
25  65 40
d

 5 , so a1  65 +10=75 .
11  3
8
Therefore, an  75  5(n  1) or an  80  5n
3. If the following sequence is geometric, find the next two terms, then write explicit and
recursive formulas for the sequence.
12,3, ________, ________
3 1
r
 , a1  12
12 4
Recursive Formula:
 12 if n  1

an   1
 4  an1 if n  1
Explicit Formula:
1
an  12   
4
n 1
4. If the following sequence is harmonic, find the next two terms, then write an explicit formula
for the sequence.
1 1 1 1
, ,  ,
3 2 7 12
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.
5
 ( 1) n 1 
a. 

 n  1 n  2
1 1 1 1
 , , ,
3 4 5 6
b.
an n 1 where
6
 3 if n is even
an   2
2n if n is odd
2,3,18,3,50,3,
c.
 an  n  5
7
where an  (i, j ) : i and j are whole number and i  j  n .
(1,5),(5,1) , (1,6),(2,3),(3, 2),(61), (1,7),(7,1)