Mathematical Investigations IV
Date 9/10/2013
S&S Unit test
Name ______________
You may use a TI-30 Calculator on this exam. Justify all your work.
n
n
n(n  1)(2n  1)
n 2 (n  1) 2
2
3
Useful formulas:
j

j



6
4
j 1
j 1
n
k=1
3,
Given ak  
and Sn   ak
k 1
2ak 1  3, k>1
a) State the first five terms
b) State the first five terms of the
1.
of the sequence an n 1 .
5
2.
sequence
Given a geometric sequence with a5  2 and a9 
Sn n 1 .
5
2
. Solve for a12 . Give exact
4
answer.
3.
The eighth term in an arithmetic sequence is 9 and the twenty-third term is 54. Find the
sum of the first twenty-three terms.
Mathematical Investigations IV
Date 9/10/2013
4.
S&S Unit test
Name ______________
Find the missing terms in the harmonic sequence:
2
15
, ________, ________, 13 .
1
1I
F
, 1  J, [an open interval]. Find a , a , and a .
G
H n nK
5.
Let a n  1 
6.
Clearly explain the difference between the sequence an  2n n 1 and the function
1
2
3

f ( x )  2 x , where x  [1, ) .
7.
n
For a given series the sequence of partial sums S n n 1 is given by Sn   ak .

k 1
Given Sn 
5n
. Find a5 .
2n  1
Mathematical Investigations IV
Date 9/10/2013
S&S Unit test

8.
x
For what values of x will the series   
k 0  3 
9.
Express in sigma-notation: 7 
10.
Evaluate each of the following.
40
a.
  5  4k 
k 1
b.
80
 k (k  2)
k  26
Name ______________
k
have a finite sum?
9 11 13
25
  
2 4 8
512
Mathematical Investigations IV
Date 9/10/2013
11.
S&S Unit test
Name ______________
A certain excavating machine can dig large holes. It can dig a suitable hole 10 feet deep
in the first hour. Since the ground gets harder to dig as you get deeper, the machine is
only able to dig 90% as many feet during each hour as the previous hour. (So it can only
dig 9 additional feet during the second hour, etc.)
a. How deep is the hole after 10 hours ?
b. What is the deepest hole that the machine can dig ?