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Chapter 14: Problem 68
A company offers a starting yearly salary of \(\$ 33,000\) with raises of \(\$ 2500\) per year. Find the total salary over a ten-year period.
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Find a general term, \(a_{n},\) for each sequence. More than one answer may be possible. $$1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \dots$$
Many graphing utilities have a sequence-graphing mode that plots the terms of a sequence as points on a rectangular coordinate system. Consult your manual; if your graphing utility has this capability, use it to graph each of the sequences in Exercises \(69-72 .\) What appears to be happening to the terms of each sequence as \(n\) gets larger? $$a_{n}=\frac{100}{n} ; n:[0,1000,100] \text { by } a_{n}:[0,1,0.1]$$
Many graphing utilities have a sequence-graphing mode that plots the terms of a sequence as points on a rectangular coordinate system. Consult your manual; if your graphing utility has this capability, use it to graph each of the sequences in Exercises \(69-72 .\) What appears to be happening to the terms of each sequence as \(n\) gets larger? $$a_{n}=\frac{2 n^{2}+5 n-7}{n^{3}}, n:[0,10,1] \text { by } a_{n}:[0,2,0.2]$$
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(10-5+\frac{5}{2}-\frac{5}{4}+\cdots=\frac{10}{1-\frac{1}{2}}\)
Use the formula for the general term (the nth term) of a geometric sequence to solve. Suppose you save \(\$ 1\) the first day of a month, \(\$ 2\) the second day, \(\$ 4\) the third day, and so on. That is, each day you save twice as much as you did the day before. What will you put aside for savings on the thirtieth day of the month?
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