Chapter 9

For the following exercises, one card is drawn from a standard deck of 52 cards. Find the probability of drawing the following: A two

Use the following scenario. Javier makes monthly deposits into a savings account. He opened the account with an initial deposit of \(\$ 50 .\) Each month thereafter he increased the previous deposit amount by \(\$ 20\). Graph the arithmetic series showing the monthly sums of one year of Javier's deposits.

For the following exercises, find the number of subsets in each given set. A set containing 5 distinct numbers, 4 distinct letters, and 3 distinct symbols

For the following exercises, use the Binomial Theorem to write the first three terms of each binomial. $$ (3 a+b)^{20} $$

For the following exercises, write a recursive formula for each geometric sequence. $$ a_{n}=\\{10,-3,0.9,-0.27, \ldots\\} $$

For the following exercises, use the recursive formula to write the first five terms of the arithmetic sequence. $$ a_{1}=-19 ; a_{n}=a_{n-1}-1.4 $$

For the following exercises, write the first five terms of the sequence. $$ a_{1}=3, a_{n}=(-3) a_{n-1} $$

For the following exercises, use the following scenario. Javier makes monthly deposits into a savings account. He opened the account with an initial deposit of \(\$ 50 .\) Each month thereafter he increased the previous deposit amount by \(\mathrm{s} 20 .\) Graph the arithmetic series showing the monthly sums of one year of Javier’s deposits.

Write the first five terms of the sequence. $$a_{1}=3, a_{n}=(-3) a_{n-1}$$

For the following exercises, one card is drawn from a standard deck of 52 cards. Find the probability of drawing the following: Six or seven

Use the geometric series \(\sum_{k=1}^{\infty}\left(\frac{1}{2}\right)^{k}\). Graph the first 7 partial sums of the series.

For the following exercises, find the number of subsets in each given set. The set of even numbers from 2 to 28

For the following exercises, use the Binomial Theorem to write the first three terms of each binomial. $$ (2 a+4 b)^{7} $$

For the following exercises, write a recursive formula for each geometric sequence. $$ a_{n}=\\{0.61,1.83,5.49,16.47, \ldots\\} $$

For the following exercises, write the first five terms of the sequence. $$ a_{1}=-4, a_{n}=\frac{a_{n-1}+2 n}{a_{n-1}-1} $$

Write the first five terms of the sequence. $$a_{1}=-4, a_{n}=\frac{a_{n-1}+2 n}{a_{n-1}-1}$$

For the following exercises, one card is drawn from a standard deck of 52 cards. Find the probability of drawing the following: Red six

Use the geometric series \(\sum_{k=1}^{\infty}\left(\frac{1}{2}\right)^{k}\). What number does \(S_{n}\) seem to be approaching in the graph? Find the sum to explain why this makes sense.

For the following exercises, find the number of subsets in each given set. The set of two-digit numbers between 1 and 100 containing the digit 0

For the following exercises, use the Binomial Theorem to write the first three terms of each binomial. $$ \left(x^{3}-\sqrt{y}\right)^{8} $$

For the following exercises, write a recursive formula for each geometric sequence. $$ a_{n}=\left\\{\frac{3}{5}, \frac{1}{10}, \frac{1}{60}, \frac{1}{360}, \ldots\right\\} $$

For the following exercises, write the first five terms of the sequence. $$ a_{1}=-1, a_{n}=\frac{(-3)^{n-1}}{a_{n-1}-2} $$

Write the first five terms of the sequence. $$a_{1}=-1, a_{n}=\frac{(-3)^{n-1}}{a_{n-1}-2}$$

For the following exercises, one card is drawn from a standard deck of 52 cards. Find the probability of drawing the following: An ace or a diamond

Find the indicated sum. $$ \sum_{a=1}^{14} a $$

For the following exercises, find the distinct number of arrangements. The letters in the word "juggernaut"

For the following exercises, find the indicated term of each binomial without fully expanding the binomial. The fourth term of \((2 x-3 y)^{4}\)

For the following exercises, write a recursive formula for each geometric sequence. $$ a_{n}=\left\\{-2, \frac{4}{3},-\frac{8}{9}, \frac{16}{27}, \ldots\right\\} $$

Write the first five terms of the sequence. $$a_{1}=-30, a_{n}=\left(2+a_{n-1}\right)\left(\frac{1}{2}\right)^{n}$$

For the following exercises, one card is drawn from a standard deck of 52 cards. Find the probability of drawing the following: A non-ace

Find the indicated sum. $$ \sum_{n=1}^{6} n(n-2) $$

For the following exercises, find the distinct number of arrangements. The letters in the word "academia"

For the following exercises, find the indicated term of each binomial without fully expanding the binomial. The fourth term of \((3 x-2 y)^{5}\)

For the following exercises, write a recursive formula for each geometric sequence. $$ a_{n}=\left\\{\frac{1}{512},-\frac{1}{128}, \frac{1}{32},-\frac{1}{8}, \ldots\right\\} $$

For the following exercises, write the first eight terms of the sequence. $$ a_{1}=\frac{1}{24}, a_{2}=1, a_{n}=\left(2 a_{n-2}\right)\left(3 a_{n-1}\right) $$

Write the first eight terms of the sequence. $$a_{1}=\frac{1}{24}, a_{2}=1, a_{n}=\left(2 a_{n-2}\right)\left(3 a_{n-1}\right)$$

Find the indicated sum. $$ \sum_{k=1}^{17} k^{2} $$

For the following exercises, one card is drawn from a standard deck of 52 cards. Find the probability of drawing the following: A heart or a non-jack

For the following exercises, find the distinct number of arrangements. The letters in the word "academia" that begin and end in "a"

For the following exercises, find the indicated term of each binomial without fully expanding the binomial. The third term of \((6 x-3 y)^{7}\)

For the following exercises, write the first five terms of the geometric sequence. $$ a_{n}=-4 \cdot 5^{n-1} $$

For the following exercises, write a recursive formula for each arithmetic sequence. $$ a=\\{-15,-7,1, \ldots\\} $$

For the following exercises, write the first eight terms of the sequence. $$ a_{1}=-1, a_{2}=5, a_{n}=a_{n-2}\left(3-a_{n-1}\right) $$

Write the first eight terms of the sequence. $$a_{1}=-1, a_{2}=5, a_{n}=a_{n-2}\left(3-a_{n-1}\right)$$

For the following exercises, two dice are rolled, and the results are summed. Construct a table showing the sample space of outcomes and sums.

Find the indicated sum. $$ \sum_{k=1}^{7} 2^{k} $$

For the following exercises, find the indicated term of each binomial without fully expanding the binomial. The eighth term of \((7+5 y)^{14}\)

For the following exercises, write the first five terms of the geometric sequence. $$ a_{n}=12 \cdot\left(-\frac{1}{2}\right)^{n-1} $$

For the following exercises, write a recursive formula for each arithmetic sequence. $$ a=\\{8.9,10.3,11.7, \ldots\\} $$

For the following exercises, write the first eight terms of the sequence. $$ a_{1}=2, a_{2}=10, a_{n}=\frac{2\left(a_{n-1}+2\right)}{a_{n-2}} $$