MATH
140 In-class Exercises on Progressions
Names_______________________________________________________
1. Consider the arithmetic progression that
begins: 4, 15, 26, …
a)
Find the next three terms________________
b)
Find the 20th term __________________
c)
Find the nth term __________________
d)
What number term is 774? __________
e)
Find the sum: 4 + 15 + 26 + …+ 774. ______________
2. The arithmetic progression of odd numbers 1,
3, 5, 7, … has some interesting properties. You need to find a general formula
for the sum of the first n terms. Try
to accomplish this by making a table of
values and guessing the formula.
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1 |
1+3 |
1+3+5 |
1+3+5+7 |
1+3+5+7+9 |
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What
do you notice about the numbers in the second row?
What
is the sum of the first n odd numbers, starting from 1? _________________
3. Now a more complex problem. We want to find a formula for the following
sum in terms of n: 
. As in problem 2 we
try a table of values and look for a pattern.
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What
kind of numbers occur in the bottom row?
______________
To
complete the problem consider the following:
The triangular numbers Tn are defined by 
For example T3 =
1 + 2 + 3 = 6. recall the formula we
derived in class: 
.
What
is your formula? 
_____________.
4. Consider the geometric progression 
with first term 1 and constant multiple 2. We need to find a formula for the sum of
this geometric progression.
a) What is the nth term of the geometric
progression 
? __________
b) Fill in the following table and try to
find the pattern that will give the formula.
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1 |
1+2 |
1+2+4 |
1+2+4+8 |
1+2+4+8+16 |
1+2+4+8+16+32 |
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c) What is 
_____________?