Question 1

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.)   $2 , - 4,6 , - 8,10 , \ldots$

Accepted Answer

A)  $a _ { n } = ( - 1 ) ^ { n + 1 } ( 2 n )$ 
B)  $a _ { n } = n ^ { 2 } + 2$ 
C)  $a _ { n } = ( - 1 ) ^ { n + 1 } ( - 2 n )$ 
D)  $a _ { n } = 2 n ^ { 2 }$ 
E)  $a _ { n } = ( - 1 ) ^ { n } ( 2 n )$ 
A)  $a _ { n } = ( - 1 ) ^ { n + 1 } ( 2 n )$ 
B)  $a _ { n } = n ^ { 2 } + 2$ 
C)  $a _ { n } = ( - 1 ) ^ { n + 1 } ( - 2 n )$ 
D)  $a _ { n } = 2 n ^ { 2 }$ 
E)  $a _ { n } = ( - 1 ) ^ { n } ( 2 n )$

Question 2

Determine the number of ways a computer can randomly generate the prime integers from 1 through 40. A prime integer

Accepted Answer

A) 10 
B) 14 
C) 12 
D) 8 
E) 16 
A) 10 
B) 14 
C) 12 
D) 8 
E) 16

Question 3

Use the Binomial Theorem to expand and simplify the expression.   $( 7 a + b ) ^ { 3 }$

Accepted Answer

A)  $343 a ^ { 3 } - 147 a ^ { 2 } b + 21 a b ^ { 2 } + b ^ { 3 }$ 
B)  $a ^ { 3 } + 147 a ^ { 2 } b + 21 a b ^ { 2 } + b ^ { 3 }$ 
C)  $343 a ^ { 3 } + 147 a ^ { 2 } b - 21 a b ^ { 2 } + b ^ { 3 }$ 
D)  $343 a ^ { 3 } + 147 a ^ { 2 } b + 21 a b ^ { 2 } - b ^ { 3 }$ 
E)  $343 a ^ { 3 } + 147 a ^ { 2 } b + 21 a b ^ { 2 } + b ^ { 3 }$ 
A)  $343 a ^ { 3 } - 147 a ^ { 2 } b + 21 a b ^ { 2 } + b ^ { 3 }$ 
B)  $a ^ { 3 } + 147 a ^ { 2 } b + 21 a b ^ { 2 } + b ^ { 3 }$ 
C)  $343 a ^ { 3 } + 147 a ^ { 2 } b - 21 a b ^ { 2 } + b ^ { 3 }$ 
D)  $343 a ^ { 3 } + 147 a ^ { 2 } b + 21 a b ^ { 2 } - b ^ { 3 }$ 
E)  $343 a ^ { 3 } + 147 a ^ { 2 } b + 21 a b ^ { 2 } + b ^ { 3 }$

Question 4

Use summation notation to write the sum.   $8 + 16 + 32 + \ldots + 1024$

Accepted Answer

A)  $\sum _ { n = 1 } ^ { 8 } 8 ( 2 ) ^ { n + 1 }$ 
B)  $\sum _ { n = 1 } ^ { 8 } 8 ( 2 ) ^ { n - 1 }$ 
C)  $\sum _ { n = 1 } ^ { 8 } 8 ( 2 ) ^ { n }$ 
D)  $\sum _ { n = 1 } ^ { 7 } 8 ( 2 ) ^ { n - 1 }$ 
E)  $\sum _ { n = 1 } ^ { 8 } ( 2 ) ^ { n - 1 }$ 
A)  $\sum _ { n = 1 } ^ { 8 } 8 ( 2 ) ^ { n + 1 }$ 
B)  $\sum _ { n = 1 } ^ { 8 } 8 ( 2 ) ^ { n - 1 }$ 
C)  $\sum _ { n = 1 } ^ { 8 } 8 ( 2 ) ^ { n }$ 
D)  $\sum _ { n = 1 } ^ { 7 } 8 ( 2 ) ^ { n - 1 }$ 
E)  $\sum _ { n = 1 } ^ { 8 } ( 2 ) ^ { n - 1 }$

Question 5

Calculate the binomial coefficient.   ${ } _ { 18 } C _ { 0 }$

Accepted Answer

A) 2 
B) 3 
C) 1 
D) 4 
E) 0 
A) 2 
B) 3 
C) 1 
D) 4 
E) 0

Question 6

Find a formula for the sum of the n terms of the sequence. $\frac { 1 } { 2 } , \frac { 5 } { 4 } , \frac { 25 } { 8 } , \frac { 125 } { 16 } , \ldots$

Accepted Answer

A)  $\frac { 5 \left( 5 ^ { n } - 2 ^ { n } \right) } { 3 \left( 2 ^ { n } \right) }$ 
B)   $\frac { 5 ^ { n - 1 } } { 2 }$ 
C)  $\frac { 5 ^ { n } + 2 ^ { n } } { 7 \left( 2 ^ { n } \right) }$ 
D)  $\frac { 1 } { 2 ^ { n } }$ 
E)  $\frac { 5 ^ { n } - 2 ^ { n } } { 3 \left( 2 ^ { n } \right) }$ 
A)  $\frac { 5 \left( 5 ^ { n } - 2 ^ { n } \right) } { 3 \left( 2 ^ { n } \right) }$ 
B)   $\frac { 5 ^ { n - 1 } } { 2 }$ 
C)  $\frac { 5 ^ { n } + 2 ^ { n } } { 7 \left( 2 ^ { n } \right) }$ 
D)  $\frac { 1 } { 2 ^ { n } }$ 
E)  $\frac { 5 ^ { n } - 2 ^ { n } } { 3 \left( 2 ^ { n } \right) }$

Question 7

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1.) $a _ { 1 } = - 7 , a _ { k + 1 } = 3 a _ { k }$

Accepted Answer

A)  $a _ { n } = - 7 n ; - 7 , - 21 , - 63 , - 189 , - 567$ 
B)  $a _ { n } = - 7 ( 3 ) ^ { n } ; - 21 , - 63 , - 189 , - 567 , - 1701$ 
C)  $a _ { n } = ( - 21 ) ^ { n } ; - 7 , - 63 , - 189 , - 567 , - 1701$ 
D)  $a _ { n } = ( - 21 ) ^ { n - 1 } ; - 21 , - 63 , - 189 , - 567 , - 1701$ 
E)  $a _ { n } = - 7 ( 3 ) ^ { n - 1 } ; - 7 , - 21 , - 63 , - 189 , - 567$ 
A)  $a _ { n } = - 7 n ; - 7 , - 21 , - 63 , - 189 , - 567$ 
B)  $a _ { n } = - 7 ( 3 ) ^ { n } ; - 21 , - 63 , - 189 , - 567 , - 1701$ 
C)  $a _ { n } = ( - 21 ) ^ { n } ; - 7 , - 63 , - 189 , - 567 , - 1701$ 
D)  $a _ { n } = ( - 21 ) ^ { n - 1 } ; - 21 , - 63 , - 189 , - 567 , - 1701$ 
E)  $a _ { n } = - 7 ( 3 ) ^ { n - 1 } ; - 7 , - 21 , - 63 , - 189 , - 567$

Question 8

Expand the expression in the difference quotient and simplify.   $\frac { f ( x + h ) - f ( x ) } { h }$ Difference quotient $f ( x ) = ( x ) ^ { 3 }$

Accepted Answer

A)  $\frac { 3 x ^ { 2 } + 3 x h + h ^ { 2 } } { h }$ 
B)  $3 x ^ { 2 } - 3 x h - h ^ { 2 }$ 
C)  $\frac { 3 x ^ { 2 } + 3 x h - h ^ { 2 } } { h }$ 
D)  $3 x ^ { 2 } + 3 x h - h ^ { 2 }$ 
E)  $3 x ^ { 2 } + 3 x h + h ^ { 2 }$ 
A)  $\frac { 3 x ^ { 2 } + 3 x h + h ^ { 2 } } { h }$ 
B)  $3 x ^ { 2 } - 3 x h - h ^ { 2 }$ 
C)  $\frac { 3 x ^ { 2 } + 3 x h - h ^ { 2 } } { h }$ 
D)  $3 x ^ { 2 } + 3 x h - h ^ { 2 }$ 
E)  $3 x ^ { 2 } + 3 x h + h ^ { 2 }$

Question 9

Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing 2 green, 6 yellow and 3 red marbles such that both marbles are yellow.

Accepted Answer

A)   $\frac { 1 } { 3 }$ 
B)   $\frac { 6 } { 5 }$ 
C)   $\frac { 36 } { 121 }$ 
D)   $\frac { 18 } { 55 }$ 
E)   $\frac { 3 } { 11 }$ 
A)   $\frac { 1 } { 3 }$ 
B)   $\frac { 6 } { 5 }$ 
C)   $\frac { 36 } { 121 }$ 
D)   $\frac { 18 } { 55 }$ 
E)   $\frac { 3 } { 11 }$

Question 10

Find the next term of the sequence. 64, 125, 216, 343, ...

Accepted Answer

A) 524 
B) 4,096 
C) 512 
D) 576 
E) none of these 
A) 524 
B) 4,096 
C) 512 
D) 576 
E) none of these

Question 11

Find a quadratic model for the sequence with the indicated terms.  
A0 = -3, a2 = 2, a4 = 10

Accepted Answer

A) an = 3
8 n2 - $\frac { 7 } { 4 }$ n - 3 
B) an = 3n2 + $\frac { 7 } { 4 }$ n + 3
8 
C) an = 3
8 n2 + $\frac { 7 } { 4 }$ n + 3 
D) an = 3
8 n2 + $\frac { 7 } { 4 }$ n - 3 
E) an = -3n2+ $\frac { 7 } { 4 }$ n + 3
8 
A) an = 3
8 n2 - $\frac { 7 } { 4 }$ n - 3 
B) an = 3n2 + $\frac { 7 } { 4 }$ n + 3
8 
C) an = 3
8 n2 + $\frac { 7 } { 4 }$ n + 3 
D) an = 3
8 n2 + $\frac { 7 } { 4 }$ n - 3 
E) an = -3n2+ $\frac { 7 } { 4 }$ n + 3
8

Question 12

Find the coefficient a of the term in the expansion of the binomial. Binomial Term $( x - 3 y ) ^ { 9 }$ $a x ^ { 5 } y ^ { 4 }$

Accepted Answer

A) a = 13 
B) a = 10206 
C) a = 45 
D) a = -19683 
E) a = 3024 
A) a = 13 
B) a = 10206 
C) a = 45 
D) a = -19683 
E) a = 3024

Question 13

Find a formula for an  for the arithmetic sequence.  
A1 = 8, a4 = 18

Accepted Answer

A) an  = $\frac { 14 } { 3 }$ + 14n 
B) an  = $\frac { 14 } { 3 }$ - 14n 
C) an  = $\frac { 10 } { 3 }$ n - $\frac { 14 } { 3 }$ 
D) an  = $\frac { 10 } { 3 }$ n + 14 
E) an  = $\frac { 10 } { 3 }$ n + $\frac { 14 } { 3 }$ 
A) an  = $\frac { 14 } { 3 }$ + 14n 
B) an  = $\frac { 14 } { 3 }$ - 14n 
C) an  = $\frac { 10 } { 3 }$ n - $\frac { 14 } { 3 }$ 
D) an  = $\frac { 10 } { 3 }$ n + 14 
E) an  = $\frac { 10 } { 3 }$ n + $\frac { 14 } { 3 }$

Question 14

Write the nth term of the geometric sequence as a function of n. $a _ { 1 } = 2 , a _ { k + 1 } = 4 a _ { k }$

Accepted Answer

A)  $a _ { n } = 2 ( 4 ) ^ { n - 1 }$ 
B)  $a _ { n } = - 2 + 4 n$ 
C)  $a _ { n } = 2 ( 4 ) ^ { n }$ 
D)  $a _ { n } = 2 \left( \frac { 1 } { 4 } \right) ^ { n - 1 }$ 
E)  $a _ { n } = 4 ( 2 ) ^ { n - 1 }$ 
A)  $a _ { n } = 2 ( 4 ) ^ { n - 1 }$ 
B)  $a _ { n } = - 2 + 4 n$ 
C)  $a _ { n } = 2 ( 4 ) ^ { n }$ 
D)  $a _ { n } = 2 \left( \frac { 1 } { 4 } \right) ^ { n - 1 }$ 
E)  $a _ { n } = 4 ( 2 ) ^ { n - 1 }$

Question 15

In a sample of 20 hand-held calculators, 15 are known to be nonfunctional.If 7 of these calculators are selected at random, what is the probability that exactly 5 in the selection are nonfunctional? Round to the nearest thousandth.

Accepted Answer

A) 0 
B) 0.714 
C) 0.387 
D) 0.467 
E) 0.750 
A) 0 
B) 0.714 
C) 0.387 
D) 0.467 
E) 0.750

Question 16

If a sequence is arithmetic, then the second differences of the sequence are all zero.

Accepted Answer

A) True 
 B)False

Question 17

Use summation notation to write the sum.   $0.9 + 3.6 + 14.4 + \ldots + 921.6$

Accepted Answer

A)  $\sum _ { n = 1 } ^ { 8 } 0.9 ( 4 ) ^ { n + 1 }$ 
B)  $\sum _ { n = 1 } ^ { 6 } ( 4 ) ^ { n - 1 }$ 
C)  $\sum _ { n = 1 } ^ { 7 } 0.9 ( 4 ) ^ { n - 1 }$ 
D)  $\sum _ { n = 1 } ^ { 8 } 0.9 ( 4 ) ^ { n }$ 
E)  $\sum _ { n = 1 } ^ { 6 } 0.9 ( 4 ) ^ { n - 1 }$ 
A)  $\sum _ { n = 1 } ^ { 8 } 0.9 ( 4 ) ^ { n + 1 }$ 
B)  $\sum _ { n = 1 } ^ { 6 } ( 4 ) ^ { n - 1 }$ 
C)  $\sum _ { n = 1 } ^ { 7 } 0.9 ( 4 ) ^ { n - 1 }$ 
D)  $\sum _ { n = 1 } ^ { 8 } 0.9 ( 4 ) ^ { n }$ 
E)  $\sum _ { n = 1 } ^ { 6 } 0.9 ( 4 ) ^ { n - 1 }$

Question 18

Find the sum of the finite geometric sequence.Round to the nearest thousandth. $\sum _ { i = 0 } ^ { 5 } 600 ( 1.05 ) ^ { i }$

Accepted Answer

A) 4081.148 
B) 3197.686 
C) 4285.205 
D) 3481.148 
E) 3315.379 
A) 4081.148 
B) 3197.686 
C) 4285.205 
D) 3481.148 
E) 3315.379

Question 19

Select the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1.)   $a _ { 1 } = 9 , a _ { k + 1 } = a _ { k } + 3$

Accepted Answer

A)  $\begin{array} { l } 
9,12,15,18,21 \
a _ { n } = 3 n + 3
\end{array}$ 
B)  $\begin{array} { l } 
9,12,15,18,21 \
a _ { n } = 6 n + 3
\end{array}$ 
C)  $\begin{array} { l } 
9,12,15,18,21 \
a _ { n } = 3 n + 6
\end{array}$ 
D)  $\begin{array} { l } 
9,12,15,18,21 \
a _ { n } = 6 n - 3
\end{array}$ 
E)  $\begin{array} { l } 
9,12,15,18,21 \
a _ { n } = 3 n - 6
\end{array}$ 
A)  $\begin{array} { l } 
9,12,15,18,21 \
a _ { n } = 3 n + 3
\end{array}$ 
B)  $\begin{array} { l } 
9,12,15,18,21 \
a _ { n } = 6 n + 3
\end{array}$ 
C)  $\begin{array} { l } 
9,12,15,18,21 \
a _ { n } = 3 n + 6
\end{array}$ 
D)  $\begin{array} { l } 
9,12,15,18,21 \
a _ { n } = 6 n - 3
\end{array}$ 
E)  $\begin{array} { l } 
9,12,15,18,21 \
a _ { n } = 3 n - 6
\end{array}$

Question 20

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) ​
An = (-2)n
​

Accepted Answer

A) ​-2, 4, -8, 16, -32Not an Arithmetic sequence 
B) -32, -16, -8, -4, -2Arithmetic sequenced = 2 
C) -2, 4, -8, 16, -32Arithmetic sequenced = -2 
D) -2, 4, -8, -16, -32Arithmetic sequenced = 2 
E) -32, -16, -8, 4, -2Not an Arithmetic sequence 
A) ​-2, 4, -8, 16, -32Not an Arithmetic sequence 
B) -32, -16, -8, -4, -2Arithmetic sequenced = 2 
C) -2, 4, -8, 16, -32Arithmetic sequenced = -2 
D) -2, 4, -8, -16, -32Arithmetic sequenced = 2 
E) -32, -16, -8, 4, -2Not an Arithmetic sequence

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) $2 , - 4,6 , - 8,10 , \ldots$

Determine the number of ways a computer can randomly generate the prime integers from 1 through 40. A prime integer

Use the Binomial Theorem to expand and simplify the expression. $( 7 a + b ) ^ { 3 }$

Use summation notation to write the sum. $8 + 16 + 32 + \ldots + 1024$

Calculate the binomial coefficient. ${ } _ { 18 } C _ { 0 }$

Find a formula for the sum of the n terms of the sequence. $\frac { 1 } { 2 } , \frac { 5 } { 4 } , \frac { 25 } { 8 } , \frac { 125 } { 16 } , \ldots$

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1.) $a _ { 1 } = - 7 , a _ { k + 1 } = 3 a _ { k }$

Expand the expression in the difference quotient and simplify. $\frac { f ( x + h ) - f ( x ) } { h }$ Difference quotient $f ( x ) = ( x ) ^ { 3 }$

Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing 2 green, 6 yellow and 3 red marbles such that both marbles are yellow.

Find the next term of the sequence. 64, 125, 216, 343, ...

Find a quadratic model for the sequence with the indicated terms. A₀ = -3, a₂ = 2, a₄ = 10

Find the coefficient a of the term in the expansion of the binomial. Binomial Term $( x - 3 y ) ^ { 9 }$ $a x ^ { 5 } y ^ { 4 }$

Find a formula for a_n for the arithmetic sequence. A₁ = 8, a₄= 18

Write the nth term of the geometric sequence as a function of n. $a _ { 1 } = 2 , a _ { k + 1 } = 4 a _ { k }$

In a sample of 20 hand-held calculators, 15 are known to be nonfunctional.If 7 of these calculators are selected at random, what is the probability that exactly 5 in the selection are nonfunctional? Round to the nearest thousandth.

If a sequence is arithmetic, then the second differences of the sequence are all zero.

Use summation notation to write the sum. $0.9 + 3.6 + 14.4 + \ldots + 921.6$

Find the sum of the finite geometric sequence.Round to the nearest thousandth. $\sum _ { i = 0 } ^ { 5 } 600 ( 1.05 ) ^ { i }$

Select the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1.) $a _ { 1 } = 9 , a _ { k + 1 } = a _ { k } + 3$

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) A_n = (-2)n

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 9: Sequences Series and Probability

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) 2,−4,6,−8,10,…2 , - 4,6 , - 8,10 , \ldots2,−4,6,−8,10,…

Determine the number of ways a computer can randomly generate the prime integers from 1 through 40. A prime integer

Use the Binomial Theorem to expand and simplify the expression. (7a+b)3( 7 a + b ) ^ { 3 }(7a+b)3

Use summation notation to write the sum. 8+16+32+…+10248 + 16 + 32 + \ldots + 10248+16+32+…+1024

Calculate the binomial coefficient. 18C0{ } _ { 18 } C _ { 0 }18​C0​

Find a formula for the sum of the n terms of the sequence. 12,54,258,12516,…\frac { 1 } { 2 } , \frac { 5 } { 4 } , \frac { 25 } { 8 } , \frac { 125 } { 16 } , \ldots21​,45​,825​,16125​,…

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1.) a1=−7,ak+1=3aka _ { 1 } = - 7 , a _ { k + 1 } = 3 a _ { k }a1​=−7,ak+1​=3ak​

Expand the expression in the difference quotient and simplify. f(x+h)−f(x)h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h)−f(x)​ Difference quotient f(x)=(x)3f ( x ) = ( x ) ^ { 3 }f(x)=(x)3

Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing 2 green, 6 yellow and 3 red marbles such that both marbles are yellow.

Find the next term of the sequence. 64, 125, 216, 343, ...

Find a quadratic model for the sequence with the indicated terms. A0 = -3, a2 = 2, a4 = 10

Find the coefficient a of the term in the expansion of the binomial. Binomial Term (x−3y)9( x - 3 y ) ^ { 9 }(x−3y)9 ax5y4a x ^ { 5 } y ^ { 4 }ax5y4

Find a formula for an for the arithmetic sequence. A1 = 8, a4 = 18

Write the nth term of the geometric sequence as a function of n. a1=2,ak+1=4aka _ { 1 } = 2 , a _ { k + 1 } = 4 a _ { k }a1​=2,ak+1​=4ak​

In a sample of 20 hand-held calculators, 15 are known to be nonfunctional.If 7 of these calculators are selected at random, what is the probability that exactly 5 in the selection are nonfunctional? Round to the nearest thousandth.

If a sequence is arithmetic, then the second differences of the sequence are all zero.

Use summation notation to write the sum. 0.9+3.6+14.4+…+921.60.9 + 3.6 + 14.4 + \ldots + 921.60.9+3.6+14.4+…+921.6

Find the sum of the finite geometric sequence.Round to the nearest thousandth. ∑i=05600(1.05)i\sum _ { i = 0 } ^ { 5 } 600 ( 1.05 ) ^ { i }∑i=05​600(1.05)i

Select the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1.) a1=9,ak+1=ak+3a _ { 1 } = 9 , a _ { k + 1 } = a _ { k } + 3a1​=9,ak+1​=ak​+3

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) ​ An = (-2)n ​

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) $2 , - 4,6 , - 8,10 , \ldots$

Use the Binomial Theorem to expand and simplify the expression. $( 7 a + b ) ^ { 3 }$

Use summation notation to write the sum. $8 + 16 + 32 + \ldots + 1024$

Calculate the binomial coefficient. ${ } _ { 18 } C _ { 0 }$

Find a formula for the sum of the n terms of the sequence. $\frac { 1 } { 2 } , \frac { 5 } { 4 } , \frac { 25 } { 8 } , \frac { 125 } { 16 } , \ldots$

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1.) $a _ { 1 } = - 7 , a _ { k + 1 } = 3 a _ { k }$

Expand the expression in the difference quotient and simplify. $\frac { f ( x + h ) - f ( x ) } { h }$ Difference quotient $f ( x ) = ( x ) ^ { 3 }$

Find a quadratic model for the sequence with the indicated terms. A₀ = -3, a₂ = 2, a₄ = 10

Find the coefficient a of the term in the expansion of the binomial. Binomial Term $( x - 3 y ) ^ { 9 }$ $a x ^ { 5 } y ^ { 4 }$

Find a formula for a_n for the arithmetic sequence. A₁ = 8, a₄= 18

Write the nth term of the geometric sequence as a function of n. $a _ { 1 } = 2 , a _ { k + 1 } = 4 a _ { k }$

Use summation notation to write the sum. $0.9 + 3.6 + 14.4 + \ldots + 921.6$

Find the sum of the finite geometric sequence.Round to the nearest thousandth. $\sum _ { i = 0 } ^ { 5 } 600 ( 1.05 ) ^ { i }$

Select the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1.) $a _ { 1 } = 9 , a _ { k + 1 } = a _ { k } + 3$

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) A_n = (-2)n