Chapter 14

Find the required term for each geo- metric sequence. The 8 th term of \(\frac{1}{2}, 1,2,4, \ldots\) 64

Solve \(A=P+P r t\) for \(P\), given that \(A=\$ 326, r=7 \%\), and \(t=9\) years.

Find the sum of the odd whole numbers between 11 and 193 , inclusive. 9384

\text { The 8th term of } \frac{243}{32}, \frac{81}{16}, \frac{27}{8}, \frac{9}{4}, \ldots, \frac{4}{9}

Eric saved a nickel the first day of a month, a dime the second day, and 20 cents the third day and then continued to double his daily savings each day for 14 days. What were his daily savings on the 14th day? What were his total savings for the 14 days? \(\quad \$ 409.60 ; \$ 819.15\)

The 7 th term of \(2,6,18,54, \ldots\) 1458

Find the 10th and 15th terms of the sequence where \(a_{n}=-n^{2}-10 . \quad a_{10}=-110, a_{15}=-235\)

Find the indicated sum \(\sum_{i=1}^{50}(3 i+5)\). 4075

The 34th term of \(7,4,1,-2, \ldots\) \(-92\)

Ms. Bryan invested \(\$ 1500\) 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. \(\$ 24,900\)

\text { The } 11 \text { th term of } 768,384,192,96, \ldots \quad \frac{3}{4}

Find the general term (the nth term) for each arithmetic sequence. $$ 11,13,15,17,19, \ldots \quad 2 n+9 $$

\text { Find the indicated sum } \sum_{i=1}^{10}(-2)^{i-1}

\text { The 10th term of }-32,16,-8,4, \ldots \quad \frac{1}{16}

5^{\prime \prime}-1 \text { is divisible by } 4

Mr. Woodley invested \(\$ 1200\) at \(11 \%\) simple interest at the beginning of each year for a period of 8 years. Find the total accumulated value of all the investments at the end of the 8-year period. \(\$ 14,352\)

$$ 7,10,13,16,19, \ldots \quad 3 n+4 $$

\text { Solve each of the following for the indicated variable. } $$ V=B h \quad \text { for } h $$

Find the sum of the infinite geometric sequence 3\. \(\frac{3}{2}, \frac{3}{4}, \frac{3}{8}, \ldots\) 6

If the 5 th term of an arithmetic sequence is \(-19\) and the 8 th term is \(-34\), find the common difference of the sequence.

6^{n}-1 \text { is divisible by } 5

An object falling from rest in a vacuum falls approximately 16 feet the first second, 48 feet the second second, 80 feet the third second, 112 feet the fourth second, and so on. How far will it fall in 11 seconds? 1936 feet

The 10th term of \(1,-2,4,-8, \ldots\) \(-512\)

$$ 2,-1,-4,-7,-10, \ldots--3 n+5 $$

Find the sum of the infinite geometric sequence for which \(a_{n}=2\left(\frac{1}{3}\right)^{n+1} \cdot \frac{1}{3}\)

If the 8th term of an arithmetic sequence is 37 and the 13 th term is 57 . find the 20 th term. 85

A raffle is organized so that the amount paid for each ticket is determined by the number on the ticket. The tickets are numbered with the consecutive odd whole numbers \(1,3,5,7, \ldots\). Each contestant pays as many cents as the number on the ticket drawn. How much money will the raffle take in if 1000 tickets are sold? \(\$ 10,000\)

\text { The 8th term of }-1,-\frac{3}{2},-\frac{9}{4},-\frac{27}{8}, \ldots-\frac{2187}{128}

$$ 4,2,0,-2,-4, \ldots \quad-2 n+6 $$

Change \(0 . \overline{18}\) to reduced \(a / b\) form, where \(a\) and \(b\) are integers and \(b \neq 0 . \quad \frac{2}{11}\)

Find the first term of a geometric sequence if the third term is 5 and the sixth term is 135 .

n^{2}+n \text { is divisible by } 2

Suppose an element has a half-life of 4 hours. This means that if \(n\) grams of it exist at a specific time, then only \(\frac{1}{2} n\) grams remain 4 hours later. If at a particular moment we have 60 grams of the element, how many grams of it will remain 24 hours later? \(\frac{15}{16}\) gram

\text { The 8th term of } \frac{1}{2}, \frac{1}{6}, \frac{1}{18}, \frac{1}{54}, \ldots, \frac{1}{4374}

$$ V=\pi r^{2} h \quad \text { for } h $$

Change \(0.2 \overline{6}\) to reduced \(a / b\) form, where \(a\) and \(b\) are integers and \(b \neq 0\). \(\quad \frac{4}{15}\)

Find the common ratio of a geometric sequence if the second term is \(\frac{1}{2}\) and the sixth term is \(8 . \quad 2\) or \(-2\)

n^{2}-n \text { is divisible by } 2

\text { The } 9 \text { th term of } \frac{16}{81}, \frac{8}{27}, \frac{4}{9}, \frac{2}{3}, \ldots . \frac{81}{16}

$$ V=\frac{1}{3} B h \quad \text { for } B $$

A tank contains 49,152 liters of gasoline. Each day, three-fourths of the gasoline remaining in the tank is pumped out and not replaced. How much gasoline remains in the tank at the end of 7 days? 3 liters

How would you describe proof by mathematical induction?

A rubber ball is dropped from a height of 1458 feet, and at each bounce it rebounds one-third of the height from which it last fell. How far has the ball traveled by the time it strikes the ground for the sixth time? 2910 feet

Find the first term of the geometric sequence with 5 th term \(\frac{32}{3}\) and common ratio 2 . \(\frac{2}{3}\)

$$ 2,6,10,14,18, \ldots \quad 4 n-2 $$

$$ C=2 \pi r \quad \text { for } r $$

Suppose that you save a dime the first day of a month, \(\$ 0.20\) the second day, and \(\$ 0.40\) the third day and that you continue to double your savings each day for 14 days. Find the total amount that you will save at the end of 14 days. \(\quad \$ 1638.30\)

Compare inductive reasoning to prove by mathematical induction.

A rubber ball is dropped from a height of 100 feet, and at each bounce it rebounds one-half of the height from which it last fell. What distance has the ball traveled up to the instant it hits the ground for the eighth time? 298 7 16 feet

$$ 2,7,12,17,22, \ldots $$ \(5 n-3\)