Math Investigations - IV
Quiz #1
SHOW ALL WORK!!
Name:____________________________
1. Find the next two terms in the sequence and then label each sequence as arithmetic,
geometric, both, or neither.
a.
1 1 5 4 11
, , , ,
, ________,
6 3 6 3 6
________
type of sequence:
b.
1 3 5 7 9
, , , , , ________,
2 4 8 16 32
________
type of sequence:
c.
1 1 1 1 1
, , , , , ________,
6 12 24 48 96
________
type of sequence:
2. Suppose an is an arithmetic sequence with a3  7 and a6  43 .
a. Find the common difference d.
b. Find the first term, a1 .
c. Write an explicit formula for an .
d. Write a recursive formula for an .
3. Write out the terms of the sequence an n 1 where an  ( x, y ) : x  n and y  2 n  .
4
4. If the following sequence is harmonic, find the next two terms, then write an explicit
formula for the sequence.
2 1
, , ________,
5 3
________
Explicit Formula:
1 if n = 1

4
5. Write out the terms of the sequence an n 1 where an  
2
2(an 1 )  an 1 if n  1
6. Suppose an is a geometric sequence with
recursive and explicit formulae for an :
Explicit:
Recursive:
a1  a3  4 and a5  8 2 . Write the