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mathematics
precalculus 1st
Precalculus 1st Edition Jay Abramson - Solutions
For the following exercises, use the Binomial Theorem to expand each binomial. (4a − b)3
For the following exercises, use the formula for the sum of the first n terms of each arithmetic sequence. 3/2 + 2 + 5/2 + 3 + 7/2
For the following exercises, write the first five terms of the geometric sequence, given the first term and common ratio. a1 = 8, r = 0.3
For the following exercises, find the specified term for the arithmetic sequence given the first term and common difference. First term is 3, common difference is 4, find the 5th term.
For the following exercises, determine whether to use the Addition Principle or the Multiplication Principle. Then perform the calculations.How many ways are there to construct a string of 3 digits if numbers cannot be repeated?
Is the sequence 4, 16, 28, 40, … geometric? If so find the common ratio. If not, explain why.
For the following exercises, write the first four terms of the sequence.an = (−10)n + 1
For the following exercises, two coins are tossed. What is the sample space?
For the following exercises, use the Binomial Theorem to expand each binomial. (5a + 2)3
For the following exercises, write the first four terms of the sequence. a n 4.(-5)"- 5
For the following exercises, use the formula for the sum of the first n terms of each arithmetic sequence.19 + 25 + 31 + … + 73
Rachael deposits $3,600 into a retirement fund each year. The fund earns 7.5% annual interest, compounded monthly. If she opened her account when she was 20 years old, how much will she have by the time she’s 55? How much of that amount was interest earned?
For the following exercises, write the first five terms of the geometric sequence, given the first term and common ratio.a1 = 5, r = 1/5
For the following exercises, compute the value of the expression. P(5, 2)
A geometric sequence has terms a7 = 16,384 and a9 = 262,144. What are the first five terms?
For the following exercises, write the first eight terms of the piecewise sequence. a₁ J(-2)" - 2 if n is even (3)" - ¹ if n is odd
For the following exercises, use the Binomial Theorem to expand each binomial. (3a + 2b)3
For the following exercises, two coins are tossed.Find the probability of tossing two heads.
For the following exercises, use the formula for the sum of the first n terms of each arithmetic sequence.3.2 + 3.4 + 3.6 + … + 5.6
For the following exercises, express each geometric sum using summation notation. 1 + 3 + 9 + 27 + 81 + 243 + 729 + 2187
In a competition of 50 professional ballroom dancers, 22 compete in the fox-trot competition, 18 compete in the tango competition, and 6 compete in both the fox-trot and tango competitions. How many dancers compete in the foxtrot or tango competitions?
For the following exercises, write the first five terms of the geometric sequence, given any two terms. a7 = 64, a10 = 512
For the following exercises, use the Binomial Theorem to expand each binomial. (2x + 3y)4
For the following exercises, find the specified term for the arithmetic sequence given the first term and common difference.First term is 5, common difference is 6, find the 8th term.
For the following exercises, compute the value of the expression.P(8, 4)
A geometric sequence has the first term a1 = −3 and common ratio r = 1/2 . What is the 8th term?
For the following exercises, two coins are tossed.Find the probability of tossing exactly one tail.
For the following exercises, express each geometric sum using summation notation.8 + 4 + 2 + … + 0.125
A buyer of a new sedan can custom order the car by choosing from 5 different exterior colors, 3 different interior colors, 2 sound systems, 3 motor designs, and either manual or automatic transmission. How many choices does the buyer have?
For the following exercises, write the first five terms of the geometric sequence, given any two terms.a6 = 25, a8 = 6.25
For the following exercises, use the Binomial Theorem to expand each binomial.(4x + 2y)5
For the following exercises, find the specified term for the arithmetic sequence given the first term and common difference.First term is 6, common difference is 7, find the 6th term.
For the following exercises, compute the value of the expression.P(3, 3)
What are the first five terms of the geometric sequence a1 = 3, an = 4 ⋅ an − 1 ?
For the following exercises, find the common difference for the arithmetic sequence provided. ,1,2,2,
What term is used to express the likelihood of an event occurring? Are there restrictions on its values? If so, what are they? If not, explain.
Is the sequence − 2, − 1, −1/2 , −1/4 , … geometric? If so find the common ratio. If not, explain why.
For the following exercises, find the common ratio for the geometric sequence.−0.125, 0.25, −0.5, 1, −2, ...
For the following exercises, evaluate the binomial coefficient. (7)
For the following exercises, find the common ratio for the geometric sequence. -2, 1 1 1 2 8' 32' 1 128'
For the following exercises, use the spinner shown in Figure 3 to find the probabilities indicated. Landing on a vowel 0 с F E Figure 3 А D В I
For the following exercises, determine whether to use the Addition Principle or the Multiplication Principle. Then perform the calculations.Let the set B = { −23, −16, −7, −2, 20, 36, 48, 72}. How many ways are there to choose a positive or an odd number from A?
An arithmetic sequence has the first term a1 = 18 and common difference d = −8. What are the first five terms?
For the following exercises, write the first four terms of the sequence.an = − 16/n + 1
For the following exercises, evaluate the binomial coefficient. (²)
For the following exercises, express each description of a sum using summation notation.The sum from of n = 0 to n = 4 of 5n
What is the 11th term of the geometric sequence − 1.5, − 3, − 6, − 12, … ?
For the following exercises, determine whether the sequence is arithmetic. If so find the common difference. {11.4, 9.3, 7.2, 5.1, 3, ... }
For the following exercises, use the spinner shown in Figure 3 to find the probabilities indicated.Not landing on blue O C F E Figure 3 A D B I
For the following exercises, determine whether to use the Addition Principle or the Multiplication Principle. Then perform the calculations.How many ways are there to pick a red ace or a club from a standard card playing deck?
An arithmetic sequence has terms a3 = 11.7 and a8 = −14.6. What is the first term?
For the following exercises, write the first four terms of the sequence.an = −(−5)n − 1
For the following exercises, evaluate the binomial coefficient. 10 (¹) 9
For the following exercises, express each description of a sum using summation notation.The sum of 6k − 5 from k = −2 to k = 1
For the following exercises, write the first four terms of the sequence. a = n 2" 3 nº
Write a recursive formula for the geometric sequence 1, − 1/2 , 1/4 , −1/8 , …
For the following exercises, determine whether the sequence is geometric. If so, find the common ratio. −6, −12, −24, −48, −96, ...
For the following exercises, use the spinner shown in Figure 3 to find the probabilities indicated.Landing on purple or a vowel O C F E Figure 3 A D B I
For the following exercises, determine whether the sequence is arithmetic. If so find the common difference.{4, 16, 64, 256, 1024, ... }
For the following exercises, determine whether to use the Addition Principle or the Multiplication Principle. Then perform the calculations.How many ways are there to pick a paint color from 5 shades of green, 4 shades of blue, or 7 shades of yellow?
For the following exercises, evaluate the binomial coefficient. 25 11
For the following exercises, express each description of a sum using summation notation.The sum that results from adding the number 4 five times
Write an explicit formula for the geometric sequence 4, − 4/3 , 4/9 , − 4/27 , …
For the following exercises, determine whether the sequence is geometric. If so, find the common ratio.5, 5.2, 5.4, 5.6, 5.8, ...
For the following exercises, write the first five terms of the arithmetic sequence given the first term and common difference. a1 = −25, d = −9
For the following exercises, determine whether to use the Addition Principle or the Multiplication Principle. Then perform the calculations.How many outcomes are possible from tossing a pair of coins?
For the following exercises, determine whether the sequence is geometric. If so, find the common ratio. -1, 1 2² 1 1 4' 8 1 16
For the following exercises, evaluate the binomial coefficient. 17 (²7) 6
Write a recursive formula for the arithmetic sequence 0, −1/2 , −1, −3/2 , … , and then find the 31st term.
For the following exercises, express each arithmetic sum using summation notation.5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50
Use summation notation to write the sum of terms 3k2 − 5/6 k from k = −3 to k = 15.
For the following exercises, use the spinner shown in Figure 3 to find the probabilities indicated.Landing on green or blue 0 с F E Figure 3 A D В I
For the following exercises, determine whether to use the Addition Principle or the Multiplication Principle. Then perform the calculations.How many outcomes are possible from tossing a coin and rolling a 6-sided die?
For the following exercises, write the first four terms of the sequence.an = 1.25 ⋅ (−4)n − 1
Write an explicit formula for the arithmetic sequence 7/8 , 29/24 , 37/24 , 15/8 , …
For the following exercises, express each arithmetic sum using summation notation.10 + 18 + 26 + … + 162
A community baseball stadium has 10 seats in the first row, 13 seats in the second row, 16 seats in the third row, and so on. There are 56 rows in all. What is the seating capacity of the stadium?
For the following exercises, determine whether the sequence is geometric. If so, find the common ratio.6, 8, 11, 15, 20, ...
For the following exercises, write the first five terms of the arithmetic series given two terms. a1 = 17, a7 = −31
For the following exercises, determine whether to use the Addition Principle or the Multiplication Principle. Then perform the calculations.How many two-letter strings—the first letter from A and the second letter from B—can be formed from the sets A = {b, c, d} and B = {a, e, i, o, u}?
What is a geometric sequence?
What is an arithmetic sequence?
Discuss the meaning of a sequence. If a finite sequence is defined by a formula, what is its domain? What about an infinite sequence?
Write the first four terms of the sequence defined by the recursive formula a1 = 2, an = an − 1 + n.
What is a binomial coefficient, and how it is calculated?
For the following exercises, assume that there are n ways an event A can happen, m ways an event B can happen, and that A and B are non-overlapping.Use the Addition Principle of counting to explain how many ways event A or B can occur.
What is an nth partial sum?
How is the common ratio of a geometric sequence found?
How is the common difference of an arithmetic sequence found?
For the following exercises, assume that there are n ways an event A can happen, m ways an event B can happen, and that A and B are non-overlapping.Use the Multiplication Principle of counting to explain how many ways event A and B can occur.
Describe three ways that a sequence can be defined.
Evaluate 6!/(5 − 3)!3!
What role do binomial coefficients play in a binomial expansion? Are they restricted to any type of number?
What is the difference between an arithmetic sequence and an arithmetic series?
Write the first four terms of the sequence defined by the explicit formula an = n2 − n − 1/n! .
What is the procedure for determining whether a sequence is geometric?
How do we determine whether a sequence is arithmetic?
Is the ordered set of even numbers an infinite sequence? What about the ordered set of odd numbers? Explain why or why not.
Write the first four terms of the sequence defined by the explicit formula an = 10n + 3.
What is the Binomial Theorem and what is its use?
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