Chapter 14

$$ \mathrm{A}=2 \pi r^{2}+2 \pi r h \quad \text { for } h $$

A woman invests \(\$ 350\) at \(12 \%\) simple interest at the beginning of each year for a period of 10 years. Find the total accumulated value of all the investments at the end of the 10 -year period. \(\$ 5810\)

Find the sum of the first 75 terms of the sequence 5,1 , \(-3,-7, \ldots\) $$ -10,725 $$

A pile of logs has 25 logs in the bottom layer, 24 logs in the next layer, 23 logs in the next layer, and so on, until the top layer has 1 log. How many logs are in the pile? 325 logs

Find the common ratio of the geometric sequence with 3 rd term 12 and 6 th term \(96.2\)

$$ -3,-6,-9,-12,-15, \ldots $$ \(-3 n\)

Find the sum of the first ten terms of the sequence where \(a_{n}=2^{5-n} .31 \frac{31}{32}\)

A well driller charges \(\$ 9.00\) per foot for the first 10 feet, \(\$ 9.10\) per foot for the next 10 feet, \(\$ 9.20\) per foot for the next 10 feet, and so on, at a price increase of \(\$ 0.10\) per foot for succeeding intervals of 10 feet. How much does it cost to drill a well to a depth of 150 feet? \$1455

Find the common ratio of the geometric sequence with 2nd term \(\frac{8}{3}\) and 5 th term \(\frac{64}{81} . \quad \frac{2}{3}\)

-4,-8,-12,-16,-20, \ldots .-4 n

$$ A=\frac{1}{2} h\left(b_{1}+b_{2}\right) \quad \text { for } h $$

\(9^{n}-1\) is divisible by 8 for all positive integer values for \(n\).

Find the sum of the first 95 terms of the sequence where $$ a_{n}=7 n+1 . \quad 32,015 $$

A pump is attached to a container for the purpose of creating a vacuum. For cach stroke of the pump, one-third of the air remaining in the container is removed. To the nearest tenth of a percent, how much of the air remains in the container after seven strokes? \(\quad 5.9 \%\)

Find the sum of the first ten terms of the geometric sequence \(1,2,4,8, \ldots\) 1023

Find the required term for each arith- metic sequence. The 15 th term of \(3,8,13,18, \ldots\) 73

$$ F=\frac{9}{5} C+32 \text { for } C $$

Find the sum \(5+7+9+\cdots+137\) 4757

Suppose that in Problem 25, each stroke of the pumpremoves one-half of the air remaining in the container. What fractional part of the air has been removed after six strokes? \(\quad \frac{63}{64}\) has been removed

Find the sum of the first seven terms of the geometric sequence \(3,9,27,81, \ldots\) 3279

The 20 th term of \(4,11,18,25, \ldots\) 137

$$ \mathrm{C}=\frac{5}{9}(F-32) \quad \text { for } \mathrm{F} $$

\text { Find the sum } 64+16+4+\cdots+\frac{1}{64} \quad 85 \frac{21}{64}

A tank contains 20 gallons of water. One-half of the water is removed and replaced with antifreeze. Then one-half of this mixture is removed and replaced with antifreeze. This process is continued eight times. How much water remains in the tank after the eighth replacement process? \(\frac{5}{64}\) gallon

Find the sum of the first nine terms of the geometric sequence \(2,6,18,54, \ldots\) 19,682

Find the sum of all even numbers between 8 and 384 , inclusive. \(\quad 37,044\)

The radiator of a truck contains 10 gallons of water. Suppose we remove 1 gallon of water and replace it with antifreeze. Then we remove 1 gallon of this mixture and replace it with antifreeze. This process is carried out seven times. To the nearest tenth of a gallon, how much antifreeze is in the final mixture? \(5.2\) gallons

Find the sum of the first ten terms of the geometric sequence \(5,10,20,40, \ldots .5115\)

The 35 th term of \(9,17,25,33 \ldots\) 281

Find the sum of all multiples of 3 between 27 and 276 , inclusive. \(\quad 12,726\)

Your friend solves Problem 6 as follows: If the car depreciates \(20 \%\) per year, then at the end of 5 years it will have depreciated \(100 \%\) and be worth zero dollars. How would you convince him that his reasoning is incorrect?

Find the sum of the first eight terms of the geometric sequence \(8,12,18,27, \ldots .394 \frac{1}{16}\)

The 52 nd term of \(1, \frac{5}{3}, \frac{7}{3}, 3, \ldots\) 35

Find each indicated sum. $$ \sum_{i=1}^{45}(-2 i+5) $$

A contractor wants you to clear some land for a housing project. He anticipates that it will take 20 working days to do the job. He offers to pay you one of two ways: (1) a fixed amount of $3000 or (2) a penny the first day, 2 cents the second day, 4 cents the third day, and so on, doubling your daily wages each day for the 20 days. Which offer should you take and why?

$$ \sum_{i=1}^{5} i^{3} \quad 225 $$

Find the sum of the first ten terms of the geometric sequence \(-4,8,-16,32, \ldots\). 1364

If the 6 th term of an arithmetic sequence is 12 and the 10 th term is 16, find the first term.

$$ a(x+b)=b(x-c) $$

Find the sum of the first nine terms of the geometric sequence \(-2,6,-18,54, \ldots .\) \(-9842\)

If the 5 th term of an arithmetic sequence is 14 and the 12 th term is 42 , find the first term.

$$ \sum_{i=4}^{75}(3 i-4) \quad 8244 $$

Find each indicated sum. 9+27+81+\cdots+729 \quad 1089

If the 3rd term of an arithmetic sequence is 20 and the 7 th term is 32 , find the 25 th term. 86

$$ \frac{x-a}{b}=c $$

If the 5 th term of an arithmetic sequence is \(-5\) and the 15 th term is \(-25\), find the 50 th term. \(-95\)

$$ \frac{x}{a}-1=b $$

Change \(0 . \overline{36}\) to reduced \(a / b\) form, where \(a\) and \(b\) are integers and \(b \neq 0\). $$ \frac{4}{11} $$

Find the sum of the first 50 terms of the arithmetic sequence \(5,7,9,11,13, \ldots\). 2700

Change \(0.4 \overline{5}\) to reduced \(a / b\) form, where \(a\) and \(b\) are integers and \(b \neq 0 . \quad \frac{41}{90}\)