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All Textbook Solutions for College Algebra (MindTap Course List)

Simplify each expression Assume that all variables represent positive numbers, and write answers without using negative exponents. (x2/3x1/3)(x2/3+x1/3)6CM 7CM 8CM 9CM 10CM 11CM 12CM 13CM 14CM 15CM 16CM 17CM 18CM 19CM 20CM 21CM 22CM 23CM 24CM 25CM 26CM 27CM 28CM 29CM 30CM 31CM 32CM 33CM 34CM 35CM 36CM 37CM 38CM 39CM 40CM 41CM 42CM 43CM 44CM 45CM 46CM 47CM 48CM 49CM 50CM 51CM 52CM 53CM 54CM 55CM 56CM 57CM 58CM 59CM 60CM 61CM 62CM 63CM 64CM Self Check Expand: (p+q)3.Self Check Expand: (pq)3.Self Check Evaluate: a. 4! b. 7!Self Check Show that 4!3!=4!.Self Check Use the Binomial Theorem to expand (p+q)4.Self Check Use the Binomial Theorem to expand (3x2y)4.Self Check Find the sixth term of the expansion in Example 7. Example 7 Find the fifth term of the expansion (a+b)11.Self Check Find the fifth term of the expansion in Example 8. Example 8 Find the sixth term of the expansion (a+b)9.9SC 1E 2E 3E 4E 5E 6E Fill in the blanks. n=n!8E 9E 10E 11E 12E 13E 14E 15E 16E 17E 18E 19E 20E Use Pascals triangle to expand each binomial. (a+b)5 22E Use Pascals triangle to expand each binomial. (xy)3 24E Use the Binomial Theorem to expand each binomial. (a+b)3 26E 27E 28E Use the Binomial theorem to expand each binomial. (2x+y)3 30E 31E 32E 33E 34E 35E 36E 37E 38E 39E 40E Find the required term in each binomial expansion. (a+b)4; 3rd term Find the required term in each binomial expansion. (ab)4; 2nd term Find the required term in each binomial expansion. (a+b)7; 5th term Find the required term in each binomial expansion. (a+b)5; 4th term Find the required term in each binomial expansion. (ab)5; 6th term Find the required term in each binomial expansion. (ab)8; 7th term Find the required term in each binomial expansion. (a+b)17; 5th term Find the required term in each binomial expansion. (ab)12; 3rd term Find the required term in each binomial expansion. (a2)4; 2nd term Find the required term in each binomial expansion. (a3)8; 3rd term Find the required term in each binomial expansion. (a+3b)9; 5th term Find the required term in each binomial expansion. (2ab)7; 4th term Find the required term in each binomial expansion. (x2+y)4; 3rd term Find the required term in each binomial expansion. (m+n2)8; 3rd term Find the required term in each binomial expansion. (r2s2)11; 10th term Find the required term in each binomial expansion. (p2q2)9; 6th term Find the required term in each binomial expansion. (a+b)n; 4th term Find the required term in each binomial expansion. (ab)n; 5th term Find the required term in each binomial expansion. (a+b)n; rth term 60E 61E 62E 63E 64E 65E 66E 67E 68E 69E Discovery and Writing If we applied the pattern of coefficients to the coefficient of the last term in Binomial Theorem, it would be n!n!(nn)!. Show that this expression equals 1.71E 72E 73E 74E 75E Critical Thinking Determine if the statement is true or false. If the statement is false, then correct it and make it true. The sum of the exponents on the variables in any term in the expansion of (a+b)555 is 555.77E 78E 79E 80E Self Check: Given an infinite sequence an=4n+7, find each of the following: a. the first five terms of the sequence b.a100 2SC 3SC 4SC 5SC 6SC 7SC 8SC 1E 2E 3E 4E 5E 6E 7E 8E 9E 10E 11E 12E 13E 14E Find the next term of each sequence 1, 6, 11, 16,Find the next term of each sequence 1, 8, 27, 64,.Find the next term of each sequence. a,a+d,a+2d,a+3d,Find the next term of each sequence a,ar,ar2,ar3,....Find the next term of each sequence 1, 3, 6, 10,.Find the next term of each sequence 20, 17, 13, 8,.Write the first five terms of each sequence and then find the specified term. an=9n1;a30 Write the first five terms of each sequence and then find the specified term an=7n+3;a14 Write the first five terms of each sequence and then find the specified term an=n2+5;a20 Write the first five terms of each sequence and then find the specified term. an=2n2+n;a13 Write the first five terms of each sequence and then find the specified term. an=n3+6;a10 Write the first five terms of each sequence and then find the specified term. an=n37;a15 Write the first five terms of each sequence and then find the specified term. an=n1n;a30 Write the first five terms of each sequence and then find the specified term an=n+13n;a15 Write the first five terms of each sequence and then find the specified term. an=(1)n4n;a8 Write the first five terms of each sequence and then find the specified term. an=(1)n5n;a9 Write the first five terms of each sequence and then find the specified term. an=(1)n+1n2;a16 Write the first five terms of each sequence and then find the specified term. an=(1)n+1n3;a11 Find the sum of the first five terms of the sequence with the given general term. an=n Find the sum of the first five terms of the sequence with the given general term. an=2n Find the sum of the first five terms of the sequence with the given general term. an=3 Find the sum of the first five terms of the sequence with the given general term. an=4n2 Find the sum of the first five terms of the sequence with the given general term. an=2(13)n Find the sum of the first five terms of the sequence with the given general term. an=(1)n Find the sum of the first five terms of the sequence with the given general term. an=3n2 Find the sum of the first five terms of the sequence with the given general term. an=2n+1 41E 42E Assume that each sequence is defined recursively. Find the first four terms of a sequence.a1=4 and an+1=an2 44E 45E 46E 47E 48E Determine whether each series is an alternating infinite series. 1+23+....+(1)nn+...50E 51E 52E 53E 54E 55E 56E 57E 58E 59E 60E 61E 62E Evaluate each sum. k=14(4k+1)2k=14(4k1)2 64E 65E 66E 67E 68E 69E 70E 71E 72E 73E 74E 75E 76E 77E 78E 79E 80E Self Check Write the first five terms and the 18th term of an arithmetic sequence with a first term of 3 and a common difference of 6.2SC 3SC 4SC 5SC 6SC Fill in the blanks. An arithmetic sequence is a sequence of the form a,a+d,a+2d,a+3d,a+d,2E 3E 4E 5E 6E 7E 8E 9E 10E 11E Practice Write the first six terms of an arithmetic sequences with the given properties a=4 and 5th term is 12.13E 14E Find the missing term in each arithmetic sequence. Find the 40th term of an arithmetic sequence with a first term of 6 and a common difference of 8.Find the missing term in each arithmetic sequence. Find the 35th term of an arithmetic sequence with a first term of 50 and a common difference of 6.Find the missing term in each arithmetic sequence. The 6th term of an arithmetic sequence is 28, and the first term is 2.Find the common difference.Find the missing term in each arithmetic sequence. The 7th term of an arithmetic sequence is 42, and the common difference is 6.Find the first term.Find the missing term in each arithmetic sequence. Find the 55th term of an arithmetic sequence whose first three terms are 8,1,and6.Find the missing term in each arithmetic sequence. Find the 37th term of an arithmetic sequence whose second and third terms are 4and6.Find the missing term in each arithmetic sequence. If the 5th term of an arithmetic sequence is 14 and the second term is 5, find the 15th term.Find the missing term in each arithmetic sequence. If the 4th term of an arithmetic sequence is 13 and the second term is 3, find the 24th term.Find the required means. Insert three arithmetic means between 10and20.Find the required means. Insert five arithmetic means between 5and15.Find the required means. Insert four arithmetic means between 7and23.Find the required means. Insert three arithmetic means between 11and2.Find the sum of the first n terms of each arithmetic series. 5+7+9+(to15terms).28E 29E 30E Solve each problem. Find the sum of the first 30 terms of an arithmetic sequence with 25th term of 10 and a common difference of 12.Solve each problem. Find the sum of the first 100 terms of an arithmetic sequence with 15th term of 86 and a first term of 2.Solve each problem Find the sum of the first 200 natural numbers.34E 35E 36E 37E 38E 39E 40E 41E Application Designing patios Each row of bricks in the following triangular patio is to have on more brick than the previous row, ending with the longest row of 150 bricks. How many bricks will be needed?Application Pile of logs Several logs are stored in pile with 20 logs on the bottom layer, 19 on the second layer, 18 on the third layer, and so on. If the top layer has one log, how many logs are in the pile?44E 45E 46E 47E 48E 49E Discovery and writing Can an arithmetic sequence be an alternating sequence? Explain.51E 52E 53E 54E 55E 56E 57E

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