 11.Test: Find the indicated term(s) of the given sequence.The first five ter...
 11.Cumulative Review: Divide.a. 204 b. 93c.  38 , 3 d. 4010e. 110 , 25 f. 80
 11.Review: (11.1) Find the indicated term(s) of the given sequence.The first f...
 11.Test: Find the indicated term(s) of the given sequence.The eightieth term...
 11.Cumulative Review: Simplify each expression.a. 3a  14a + 32b. 15x  32 + 12x + 62c. 4...
 11.Review: (11.1) Find the indicated term(s) of the given sequence.The first f...
 11.Test: Find the indicated term(s) of the given sequence.The general term o...
 11.Cumulative Review: Suppose that a computer store just announced an 8% decreasein the p...
 11.Review: (11.1) Find the indicated term(s) of the given sequence.The onehun...
 11.Test: Find the indicated term(s) of the given sequence.The general term o...
 11.Cumulative Review: Sara bought a digital camera for $344.50 including tax. If thetax r...
 11.Review: (11.1) Find the indicated term(s) of the given sequence.The fiftiet...
 11.Test: Find the partial sum of the given sequence.S5 of the sequence an = ...
 11.Cumulative Review: Solve: 3y  2x = 7 for y.
 11.Review: (11.1) Find the indicated term(s) of the given sequence.The general...
 11.Test: Find the partial sum of the given sequence.S30 of the sequence an =...
 11.Cumulative Review: Find an equation of the line through 13, 22 and parallel to3x  2y...
 11.Review: (11.1) Find the indicated term(s) of the given sequence.The general...
 11.Test: Find the partial sum of the given sequence.S of the sequence a1 = 2...
 11.Cumulative Review: Use the product rule to simplify.a. 13x6215x2 b. 1 2.4x3p2214xp102
 11.Review: Solve the following applications.The distance in feet that an olive...
 11.Test: Find the partial sum of the given sequence.S of the sequence 32,  ...
 11.Cumulative Review: Solve: y3 + 5y2  y = 5
 11.Review: Solve the following applications.A culture of yeast measures 80 and...
 11.Test: Find the partial sum of the given sequence.a4i=1i1i  22
 11.Cumulative Review: Use synthetic division to divide x4  2x3  11x2 + 34 byx + 2.
 11.Review: Solve the following applications.The Colorado Forest Service report...
 11.Test: Find the partial sum of the given sequence.a4i=25122i1 12i
 11.Cumulative Review: Perform the indicated operation and simplify if possible.53a  6  ...
 11.Review: Solve the following applications.The first row of an amphitheater c...
 11.Test: Expand each binomial 1a  b26
 11.Cumulative Review: Simplify the following.a. 250 b. 23 24c. 226 d. 24 32
 11.Review: Find the first five terms of the geometric sequence whosefirst term...
 11.Test: Expand each binomial12x + y25
 11.Cumulative Review: Solve: 23x + 6  27x  6 = 0
 11.Review: Find the first five terms of the arithmetic sequence whosefirst ter...
 11.Test: Solve the following applications.The population of a small town is ...
 11.Cumulative Review: Use the formula A = P11 + r2t to find the interest rate r if$2000 c...
 11.Review: Find the thirtieth term of the arithmetic sequence whosefirst term ...
 11.Test: Solve the following applications.A gardener is making a triangular ...
 11.Cumulative Review: Rationalize each denominator.a. A3 43x b. 22 + 122  1
 11.Review: Find the eleventh term of the arithmetic sequence whosefirst term i...
 11.Test: Solve the following applications.A pendulum swings through an arc o...
 11.Cumulative Review: Solve: 1x  322  31x  32  4 = 0.
 11.Review: Find the twentieth term of the arithmetic sequence whosefirst three...
 11.Test: Solve the following applications.See Exercise 15. Find the total ar...
 11.Cumulative Review: Solve: 1012x + 422  12x + 4 = 3
 11.Review: Find the sixth term of the geometric sequence whose firstthree term...
 11.Test: Solve the following applications.A parachutist in freefall falls 1...
 11.Cumulative Review: Solve: 5 x + 1 6 2.
 11.Review: If the fourth term of an arithmetic sequence is 18 and thetwentieth...
 11.Test: Solve the following applications.Use the formula S to write 0.4242 ...
 11.Cumulative Review: Graph f 1x2 = 1x + 222  6. Find the vertex and axis ofsymmetry.
 11.Review: If the third term of a geometric sequence is 48 and thefourth term...
 11.Cumulative Review: A rock is thrown upward from the ground. Its height infeet above gr...
 11.Review: Find the general term of the sequence 310, 3100, 31000,c.
 11.Cumulative Review: Find the vertex of f1x2 = x2 + 3x  18.
 11.Review: Find a general term that satisfies the terms shown for the sequence...
 11.Cumulative Review: If f 1x2 = x2 and g1x2 = x + 3, find each composition.a. 1f g2122 a...
 11.Review: Determine whether each of the following sequences is arithmetic, ge...
 11.Cumulative Review: Find the inverse of f1x2 = 2x + 3.
 11.Review: Determine whether each of the following sequences is arithmetic, ge...
 11.Cumulative Review: Find the inverse of the onetoone function f = 510, 12, 1 2, 72, ...
 11.Review: Determine whether each of the following sequences is arithmetic, ge...
 11.Cumulative Review: If f 1x2 = x2  2 and g1x2 = x + 1, find each composition.a. 1f g21...
 11.Review: Determine whether each of the following sequences is arithmetic, ge...
 11.Cumulative Review: Solve each equation for x.a. 2x = 16 b. 9x = 27 c. 4x+3 = 8x
 11.Review: Solve the following applicationsTo test the bounce of a racquetball...
 11.Cumulative Review: Solve each equation.a. log2 32 = x b. log4164 = xc. log1/2 x = 5
 11.Review: Solve the following applicationsA display of oil cans in an auto pa...
 11.Cumulative Review: Simplify.a. log3 32 b. log7 71c. 5log5 3 d. 2log2 6
 11.Review: Solve the following applicationsSuppose that you save $1 the first ...
 11.Cumulative Review: Solve each equation for x.a. 4x = 64 b. 8x = 32c. 9x+4 = 243x
 11.Review: Solve the following applicationsOn the first swing, the length of a...
 11.Cumulative Review: Write each sum as a single logarithm.a. log11 10 + log11 3b. log312...
 11.Review: Solve the following applicationsRosa takes a job that has a monthly...
 11.Cumulative Review: Find the exact value.a. log 100,000 b. log 103c. ln 25 e d. ln e4
 11.Review: Solve the following applicationsA sheet of paper is 1512@inch thick...
 11.Cumulative Review: Find the amount owed at the end of 5 years if $1600 is loaned ata r...
 11.Review: (11.3) Write out the terms and find the sum for each of the followi...
 11.Cumulative Review: Write each expression as a single logarithm.a. log6 5 + log6 4b. lo...
 11.Review: (11.3) Write out the terms and find the sum for each of the followi...
 11.Cumulative Review: Solve: 3x = 7.
 11.Review: (11.3) Write out the terms and find the sum for each of the followi...
 11.Cumulative Review: Using A = Pa1 + rn bnt, find how long it takes $5000 todouble if it...
 11.Review: (11.3) Write out the terms and find the sum for each of the followi...
 11.Cumulative Review: Solve: log41x  22 = 2
 11.Review: Write the sum with notation1 + 3 + 9 + 27 + 81 + 243
 11.Cumulative Review: Solve: log4 10  log4 x = 2.
 11.Review: Write the sum with notation6 + 2 + 1 22 + 1 62 + 1 102 + 1 142 ...
 11.Cumulative Review: Graph x216  y225 = 1.
 11.Review: Write the sum with notation4+116+164+1256
 11.Cumulative Review: Find the distance between 18, 52 and 1 2, 42.
 11.Review: Write the sum with notation + a  32b +94
 11.Cumulative Review: Solve the system e y = 2xx2 + y2 = 6
 11.Review: Solve.A yeast colony begins with 20 yeast and doubles every 8hours....
 11.Cumulative Review: Solve the system ex2 + y2 = 36x  y = 6
 11.Review: Solve.The number of cranes born each year in a new aviary forms ase...
 11.Cumulative Review: Graph x29+ y216 1.
 11.Review: Solve.Harold has a choice between two job offers. Job A has an annu...
 11.Cumulative Review: Graph ey x2y 4 .
 11.Review: Solve.A sample of radioactive waste is decaying such that the amoun...
 11.Cumulative Review: Write the first five terms of the sequence whose generalterm is giv...
 11.Review: (11.4) Find the partial sum of the given sequenceS4 of the sequence...
 11.Cumulative Review: If the general term of a sequence is an = nn + 4, find a8.
 11.Review: (11.4) Find the partial sum of the given sequenceS6 of the sequence...
 11.Cumulative Review: Find the eleventh term of the arithmetic sequence whosefirst three ...
 11.Review: (11.4) Find the partial sum of the given sequence S5 of the sequenc...
 11.Cumulative Review: Find the sixth term of the geometric sequence 2, 10, 50, c.
 11.Review: (11.4) Find the partial sum of the given sequenceS3 of the sequence...
 11.Cumulative Review: Evaluate.a. a6i=0i  22 b. a5i=32i
 11.Review: (11.4) Find the partial sum of the given sequenceThe sixth partial ...
 11.Cumulative Review: Evaluate.a. a4i=0i1i + 12 b. a3i=02i
 11.Review: (11.4) Find the partial sum of the given sequenceThe ninth partial ...
 11.Cumulative Review: Find the sum of the first 30 positive integers.
 11.Review: (11.4) Find the partial sum of the given sequenceThe sum of the fir...
 11.Cumulative Review: Find the third term of the expansion of 1x  y26
 11.Review: (11.4) Find the partial sum of the given sequenceThe sum of the fir...
 11.Review: (11.4) Find the partial sum of the given sequenceThe sum of the fir...
 11.Review: (11.4) Find the partial sum of the given sequenceThe sum of the fir...
 11.Review: (11.4) Find the partial sum of the given sequenceS4 if a1 = 6 and r...
 11.Review: (11.4) Find the partial sum of the given sequenceS100 if a1 = 3 an...
 11.Review: Find the sum of each infinite geometric sequence5, 52,54,c
 11.Review: Find the sum of each infinite geometric sequence18, 2,29,c
 11.Review: Find the sum of each infinite geometric sequence20, 4,  45,c
 11.Review: Find the sum of each infinite geometric sequence0.2, 0.02, 0.002,c
 11.Review: Solve.A frozen yogurt store owner cleared $20,000 the first year he...
 11.Review: Solve.On his first morning in a television assembly factory, a trai...
 11.Review: Solve.During the harvest season, a farmer can rent a combine machin...
 11.Review: Solve.A rubber ball is dropped from a height of 15 feet and rebound...
 11.Review: Solve.After a pond was sprayed once with insecticide, 1800 mosquito...
 11.Review: Solve. See Exercise 63. Find the day on which the insecticide is no...
 11.Review: Solve.Use the formula S to write 0.555 as a fraction.
 11.Review: Solve.A movie theater has 27 seats in the first row, 30 seats in th...
 11.Review: (11.5) Use Pascals triangle to expand each binomial.1x + z25
 11.Review: (11.5) Use Pascals triangle to expand each binomial.1y  r26
 11.Review: (11.5) Use Pascals triangle to expand each binomial.12x + y24
 11.Review: (11.5) Use Pascals triangle to expand each binomial.13y  z24
 11.Review: Use the binomial formula to expand the following.1b + c28
 11.Review: Use the binomial formula to expand the following.1x  w27
 11.Review: Use the binomial formula to expand the following.14m  n24
 11.Review: Use the binomial formula to expand the following.1p  2r25
 11.Review: Find the indicated termThe fourth term of the expansion of 1a + b27
 11.Review: Find the indicated termThe eleventh term of the expansion of 1y + 2...
 11.Review: Find the indicated termEvaluate: a4i=1i21i + 12
 11.Review: Find the indicated termFind the fifteenth term of the arithmetic se...
 11.Review: Find the indicated termFind the sum of the infinite geometric seque...
 11.Review: Find the indicated termExpand: 12x  324
Solutions for Chapter 11: Sequences, Series, and the Binomial Theorem
Full solutions for Intermediate Algebra  6th Edition
ISBN: 9780321785046
Solutions for Chapter 11: Sequences, Series, and the Binomial Theorem
Get Full SolutionsThis textbook survival guide was created for the textbook: Intermediate Algebra, edition: 6. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 11: Sequences, Series, and the Binomial Theorem includes 148 full stepbystep solutions. Intermediate Algebra was written by and is associated to the ISBN: 9780321785046. Since 148 problems in chapter 11: Sequences, Series, and the Binomial Theorem have been answered, more than 59595 students have viewed full stepbystep solutions from this chapter.

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Solvable system Ax = b.
The right side b is in the column space of A.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).