M120 Project on Sequences and Series
Date due: [5 point penalty for each class late]
Objective: Sequence and Series Ownership
Sequences
1. Enter each of the following sequences
into your calculator as a function of x, where x only takes
values of1, 2, 3, …Evaluate and record the sequence for increasing values of n. Determine if the sequence converges (has
a limit) or diverges. If it
converges, find its limit.
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2. Find a formula for the nth term
of the sequence. Then, based on
your formulas, decide whether the sequence converses or diverges.
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3. Federal Debt. It took more than 200 years for the
U.S. to accumulate a $1 trillion debt.
Then it took just 8 years to get to a $3 trillion. The federal debt during the decade of the
1980's is approximated by the model 
, n = 0, 1, 2, …, 10, where 
is the debt in
trillions and n is the year, with n = 0 corresponding to
1980.Find the terms of this finite sequence and construct a bar graph that represents
the sequence (Source: Treasury
Department)
Series
Use the sum( seq( rule, variable, start, stop))function of your calculator to decide whether each series converges or diverges .If it appears to converge, what is its sum? Note: Be careful about the starting value of n. Sometimes it is 0 and sometimes it is 1.
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5. Drilling Costs A well drilling company charges $16 for drilling the first foot of a well, $16.10 for drilling the second foot, $16.20 for the third foot, and so on. Determine the cost of drilling a 100-foot well.
a) Find a formula for the cost of the nth foot.
b) Express the total cost using the
summation 
notation.
c) Find the sum (i.e., the total cost of drilling a 100-foot well.)