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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

What is the Binomial Theorem and what is its use?
What is an experiment?
Is the sequence 0.3, 1.2, 2.1, 3, … arithmetic? If so find the common difference.
What is the difference between an arithmetic sequence and a geometric sequence?
What are the main differences between using a recursive formula and using an explicit formula to describe an arithmetic sequence?
Answer the following questions. Describe how the permutation of n objects differs from the permutation of choosing r objects from a set of n objects. Include how each is calculated.
What happens to the terms an of a sequence when there is a negative factor in the formula that is raised to a power that includes n? What is the term used to describe this phenomenon?
Write the first four terms of the sequence defined by the explicit formula an = n!/n(n + 1).
When is it an advantage to use the Binomial Theorem? Explain.
What is the difference between events and outcomes? Give an example of both using the sample space of tossing a coin 50 times.
For the following exercises, evaluate the binomial coefficient. 6 (3) 2
How is finding the sum of an infinite geometric series different from finding the nth partial sum?
An arithmetic sequence has the first term a1 = −4 and common difference d = −4/3 . What is the 6th term?
Write a recursive formula for the arithmetic sequence −2, −7/2 , − 5, −13/2 , … and then find the 22nd term.
Describe how exponential functions and geometric sequences are similar. How are they different?
Describe how linear functions and arithmetic sequences are similar. How are they different?
Answer the following questions. What is the term for the arrangement that selects r objects from a set of n objects when the order of the r objects is not important? What is the formula for
Is the sequence 4/7 , 47/21 , 82/21 , 39/7 , ... arithmetic? If so,find the common difference.
What is a factorial, and how is it denoted? Use an example to illustrate how factorial notation can be beneficial.
For the following exercises, evaluate the binomial coefficient. 5 3
The union of two sets is defined as a set of elements that are present in at least one of the sets. How is this similar to the definition used for the union of two events from a probability model?
Write an explicit formula for the arithmetic sequence 15.6, 15, 14.4, 13.8, … and then find the 32nd term.
For the following exercises, find the common ratio for the geometric sequence. 1, 3, 9, 27, 81, ...
For the following exercises, use the spinner shown in Figure 3 to find the probabilities indicated. Landing on red O C F E Figure 3 A D B I
For the following exercises, find the common difference for the arithmetic sequence provided. {5, 11, 17, 23, 29, ... }
For the following exercises, determine whether to use the Addition Principle or the Multiplication Principle. Then perform the calculations. Let the set A = { −5, −3, −1, 2, 3, 4, 5, 6}.
Is the sequence 2, 4, 8, 16, ... arithmetic? If so, find the common difference.
For the following exercises, write the first four terms of the sequence. an = 2n − 2
For the following exercises, express each description of a sum using summation notation. The sum of terms m2 + 3m from m = 1 to m = 5
For the following exercises, write a recursive formula for each sequence.2, 4, 12, 48, 240, …
For the following exercises, write a recursive formula for each sequence.35, 38, 41, 44, 47, …
For the following exercises, use the formula for the sum of the first n terms of a geometric series to find the partial sum.S6 for the series −2 − 10 − 50 − 250 ...
For the following exercises, write an explicit formula for each geometric sequence.an = {−1.25, −5, −20, −80, ...}
For the following exercises, find the distinct number of arrangements.Suppose a set A has 2,048 subsets. How many distinct objects are contained in A?
For the following exercises, use the recursive formula to write the first five terms of the arithmetic sequence.a = {7, 4, 1, ... }; Find the 17th term.
For the following exercises, write a recursive formula for each arithmetic sequence. a= { ² ₂ ² 11 12' -2,..
For the following exercises, write a recursive formula for each sequence. 15, 3, 3 3 3 5' 25' 125 yw
For the following exercises, use the formula for the sum of the first n terms of a geometric series to find the partial sum.S7 for the series 0.4 − 2 + 10 − 50 ...
For the following exercises, write an explicit formula for each geometric sequence. 4 16 64 9,₁ = (-1₁ -₁ -2 5²-525) {1, a 5 125'
For the following exercises, find the distinct number of arrangements.How many arrangements can be made from the letters of the word “mountains” if all the vowels must form a string?
For the following exercises, use the recursive formula to write the first five terms of the arithmetic sequence.a = {4, 11, 18, ... }; Find the 14th term.
For the following exercises, evaluate the factorial. 6!
For the following exercises, use the formula for the sum of the first n terms of a geometric series to find the partial sum. Σ k=1 2k-1
For the following exercises, write an explicit formula for each geometric sequence. 1 1 3' 18' a₁ = { 2² ₁ 1 1 ₁ 1 1 108'
For the following exercises, use the formula for the sum of the first n terms of a geometric series to find the partial sum. 10 Σ- n=1 -2. 2 n-1
For the following exercises, find the distinct number of arrangements.A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in the front and 3 in the back.a.
For the following exercises, use the recursive formula to write the first five terms of the arithmetic sequence.a = {2, 6, 10, ... }; Find the 12th term.
For the following exercises, evaluate the factorial.(12/6)!
For the following exercises, write an explicit formula for each geometric sequence. a ‚= {3,-1, -Im 3 }....}
For the following exercises, find the distinct number of arrangements.The symbols in the string #,#,#,@,@,$,$,$,%,%,%,%
For the following exercises, write a recursive formula for each arithmetic sequence.a = {8.9, 10.3, 11.7, ... }
For the following exercises, write an explicit formula for each geometric sequence. an = {−2, −4, −8, −16, ...}
For the following exercises, use the formula for the sum of the first n terms of an arithmetic series to find the sum. −1.7 + −0.4 + 0.9 + 2.2 + 3.5 + 4.8
For the following exercises, find the distinct number of arrangements.The symbols in the string #,#,#,@,@,$,$,$,%,%,%,% that begin and end with “%”
For the following exercises, write a recursive formula for each arithmetic sequence.a = {−0.52, −1.02, −1.52, ... }
For the following exercises, write a recursive formula for each sequence. −2.5, − 5, − 10, − 20, − 40, …
For the following exercises, use the formula for the sum of the first n terms of an arithmetic series to find the sum. 15 6+ +9+ 2 21 2 + 12 + 27 2 +15
For the following exercises, write an explicit formula for each geometric sequence.an = {1, 3, 9, 27, ...}
For the following exercises, write a recursive formula for each arithmetic sequence. a = 19 7 5' 20' 20' 10
For the following exercises, find the distinct number of arrangements.The set, S consists of 900,000,000 whole numbers, each being the same number of digits long. How many digits long is a number
For the following exercises, write a recursive formula for each sequence.−8, − 6, − 3, 1, 6, …
For the following exercises, use the formula for the sum of the first n terms of an arithmetic series to find the sum.−1 + 3 + 7 + ... + 31
For the following exercises, write a recursive formula for each arithmetic sequence. 5 a = { - 1/² - 1/2 2 -2,...
For the following exercises, write an explicit formula for each geometric sequence.an = {−4, −12, −36, −108, ...}
For the following exercises, find the distinct number of arrangements.The number of 5-element subsets from a set containing n elements is equal to the number of 6-element subsets from the same set.
For the following exercises, use the formula for the sum of the first n terms of an arithmetic series to find the sum. k = 1 k 2 1 2/
For the following exercises, write an explicit formula for each geometric sequence.an = {0.8, −4, 20, −100, ...}
For the following exercises, find the distinct number of arrangements.Can C(n, r) ever equal P(n, r)? Explain.
For the following exercises, find the distinct number of arrangements.A cell phone company offers 6 different voice packages and 8 different data packages. Of those, 3 packages include both voice and
For the following exercises, use the recursive formula to write the first five terms of the arithmetic sequence.a = 24 − 4n
For the following exercises, find the sum of the infinite geometric series.4 + 2 + 1 + 1/2 ...
For the following exercises, evaluate the factorial.12!/6!
For the following exercises, find the distinct number of arrangements.In horse racing, a “trifecta” occurs when a bettor wins by selecting the first three finishers in the exact order (1st place,
For the following exercises, find the specified term for the geometric sequence given. Let a1 = 4, an = −3an − 1 . Find a8.
For the following exercises, find the sum of the infinite geometric series. -1 1 4 1 1 16 1 64
For the following exercises, use the recursive formula to write the first five terms of the arithmetic sequence.a = 1/2 n − 1/2
For the following exercises, evaluate the factorial.100!/99!
For the following exercises, find the specified term for the geometric sequence given. n-1 = ( - } ). Find a 12 . 3 Let a
For the following exercises, find the distinct number of arrangements.A wholesale T-shirt company offers sizes small, medium, large, and extra-large in organic or nonorganic cotton and colors white,
For the following exercises, write an explicit formula for each arithmetic sequence. a = {3, 5, 7, ... }
For the following exercises, find the sum of the infinite geometric series. k=1 Σ3 Y 4 |k-1
For the following exercises, write the first four terms of the sequence. an = n!/n2
For the following exercises, find the number of terms in the given finite geometric sequence. an = {−1, 3, −9, ... , 2187}
For the following exercises, find the distinct number of arrangements.Hector wants to place billboard advertisements throughout the county for his new business. How many ways can Hector choose 15
For the following exercises, write the first four terms of the sequence. a n 3.n! 4.n!
For the following exercises, write an explicit formula for each arithmetic sequence.a = {32, 24, 16, ... }
For the following exercises, find the sum of the infinite geometric series. Σ46.0.5"-1 n=1
For the following exercises, find the number of terms in the given finite geometric sequence. 1 1024 a₁ ₁ = {2, 1, 1/12 - 1
For the following exercises, find the distinct number of arrangements.An art store has 4 brands of paint pens in 12 different colors and 3 types of ink. How many paint pens are there to choose from?
For the following exercises, write an explicit formula for each arithmetic sequence.a = {−5, 95, 195, ... }
For the following exercises, write the first four terms of the sequence. a n n! n²-n-1
For the following exercises, determine whether the graph shown represents a geometric sequence. an 6- 5 4 3 2 1 . (5,5) . (1, -3) . (4,3) .(3, 1) + +n -0.50 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
For the following exercises, determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate. Deposit amount: $50; total deposits: 60;
For the following exercises, write the first four terms of the sequence. a n 100 - n n(n − 1)!
For the following exercises, find the distinct number of arrangements.How many ways can a committee of 3 freshmen and 4 juniors be formed from a group of 8 freshmen and 11 juniors?
For the following exercises, write an explicit formula for each arithmetic sequence.a = {−17, −217, −417, ... }
For the following exercises, determine whether the graph shown represents a geometric sequence. an 6+ 5.5+ 5+ 4.5+ 4 3.5+ 3+ 2.5+ 2 1.5 1 نیا 0.5 -0.5 0 -0.5 -1 • (5, 5.5938) . (4, 3.0625) . (3,
For the following exercises, determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate.Deposit amount: $150; total deposits: 24;
For the following exercises, find the distinct number of arrangements.How many ways can a baseball coach arrange the order of 9 batters if there are 15 players on the team?
For the following exercises, graph the first five terms of the indicated sequence a = n (-1)" n + n

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