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
1.
3, if k  1 or k  2
Given ak  
2ak 1  ak  2 , k  2
a) State the terms of the
4
sequence an n 1 .
2.
Given a harmonic sequence with a5 
n
and
Sn   ak
k 1
b) State the terms of the
4
sequence S n n 1 .
15
15
and a8  . Solve for a12 . Give the exact
2
11
answer.
3.
5
The third term in a geometric sequence is 10 and the seventh term is . Find an explicit
8
formula for this sequence.
Mathematical Investigations IV
Date 9/10/2013
S&S Unit test
Name
4.
Find the sum of the arithmetic series a1 + a2 + a3 + ...+ a52 given a2  12 and a52  138 .
5.
Let an  {( x, y) x  2n and y  3n} . Write out the terms of
6.
For a given series the sequence of partial sums S n n 1 is given by Sn   ak .

an n  2
5
.
n
k 1
Given Sn  3n  n . Find a5 .
2
7.
Express in sigma-notation: 3-
7 11 15
+ - +
4 9 16
-
79
400
Mathematical Investigations IV
Date 9/10/2013
S&S Unit test
Name
8. Vivian goes home for the weekend and her friend asks her what she is studying in math.
Vivian says sequences like:
and so on. Her friend says that is not right because she knows sequences are lists of numbers like
1 1 1 1
, , , ,...
2 4 8 16
If you were Vivian, what would you say to convince her friend that she is correct? Your answer
should demonstrate you understanding of the definition of a sequence.
9.
Evaluate each of the following.
a.
50
  5  4k 
k 8
b.
80
 k 2 (k  2)
k 1
Mathematical Investigations IV
Date 9/10/2013
10.
S&S Unit test
Name
After one minute, a hot air balloon had risen 90 feet. Each succeeding minute after
that time, the balloon rose 70% as far as it did during the previous minute.
a. How far above the earth was the balloon after 8 minutes?
b. What is the maximum height the balloon will rise?

11.
For what values of x will the series
  x  3
k 0
k
have a finite sum?