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Chapter 14: Problem 71
A section in a stadium has 20 seats in the first row, 23 seats in the second row, increasing by 3 seats each row for a total of 38 rows. How many seats are in this section of the stadium?
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Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The sum of the geometric series \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\dots+\frac{1}{512}\) can only be estimated without knowing precisely what terms occur between \(\frac{1}{8}\) and \(\frac{1}{512}\).
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 sum of the first n terms of a geometric sequence to solve. A pendulum swings through an arc of 20 inches. On each successive swing, the length of the arc is \(90 \%\) of the previous length. $$\begin{aligned}&20, \quad\quad 0.9(20), \quad0.9^{2}(20), \quad 0.9^{3}(20), \ldots\\\&\begin{array}{|c|c|c|c|}\hline \text { 1st } & \text { 2nd } & \text { 3rd } & \text { 4th } \\\\\text { swing } & \text { swing } & \text { swing } & \text { swing } \\\\\hline\end{array}\end{aligned}$$ After 10 swings, what is the total length of the distance the pendulum has swung? Round to the nearest hundredth of an inch.
Use the formula for the sum of the first n terms of a geometric sequence to solve. You save \(\$ 1\) the first day of a month, \(\$ 2\) the second day, \(\$ 4\) the third day, continuing to double your savings each day. What will your total savings be for the first 30 days?
Find a general term, \(a_{n},\) for each sequence. More than one answer may be possible. $$\frac{3}{2}, \frac{4}{3}, \frac{5}{4}, \frac{6}{5}, \dots$$
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