Question 1

Determine whether the expression is a partial sum of an arithmetic or geometric sequence. Then find the sum. $5 + 25 + 125 +\dots + 3125$

Accepted Answer

A)  $19530$ 
B)  $7810$ 
C)  $3125$ 
D)  $3280$ 
E)  $3905$ 
A)  $19530$ 
B)  $7810$ 
C)  $3125$ 
D)  $3280$ 
E)  $3905$

Question 2

Find the amount of an annuity that consists of $30$ annual payments of $\$ 500$
Each into an account that pays $7 \%$
Interest per year

Accepted Answer

A)  $\$ 7,230.09$ 
B)  $\$ 17,230.49$ 
C)  $\$ 47,230.39$ 
D)  $\$ 15,000$ 
E)  $\$ 37,430.59$ 
A)  $\$ 7,230.09$ 
B)  $\$ 17,230.49$ 
C)  $\$ 47,230.39$ 
D)  $\$ 15,000$ 
E)  $\$ 37,430.59$

Question 3

Determine whether the expression is a partial sum of an arithmetic or geometric sequence. Then find the sum. $5 + 25 + 125 + \dots + 3125$

Accepted Answer

A)  $19530$ 
B)  $7810$ 
C)  $3125$ 
D)  $3280$ 
E)  $3905$ 
A)  $19530$ 
B)  $7810$ 
C)  $3125$ 
D)  $3280$ 
E)  $3905$

Question 4

Find the first four terms of the sequence $a _ { n } = n - 2$

Accepted Answer

A)  $a _ { 1 } = - 1$, $a _ { 2 } = 0$, $a _ { 3 } = 1$, $a _ { 4 } = 2$ 
B)  $a _ { 1 } = 0$, $a _ { 2 } = 1$, $a = 2$, $a _ { 4 } = 3$ 
C)  $a _ { 1 } = - 2$, $a _ { 2 } = - 3$, $a _ { 3 } = - 4$, $a _ { 4 } = - 5$ 
D)  $a _ { 1 } = 1$, $a _ { 2 } = 2$, $a = 3$, $a _ { 4 } = 4$ 
E)  $a _ { 1 } = 2$, $a _ { 2 } = 3$, $a _ {3 } = 4$, $a _ { 4 } = 5$ 
A)  $a _ { 1 } = - 1$, $a _ { 2 } = 0$, $a _ { 3 } = 1$, $a _ { 4 } = 2$ 
B)  $a _ { 1 } = 0$, $a _ { 2 } = 1$, $a = 2$, $a _ { 4 } = 3$ 
C)  $a _ { 1 } = - 2$, $a _ { 2 } = - 3$, $a _ { 3 } = - 4$, $a _ { 4 } = - 5$ 
D)  $a _ { 1 } = 1$, $a _ { 2 } = 2$, $a = 3$, $a _ { 4 } = 4$ 
E)  $a _ { 1 } = 2$, $a _ { 2 } = 3$, $a _ {3 } = 4$, $a _ { 4 } = 5$

Question 5

The first four terms of a sequence are given. Determine whether they can be terms of an arithmetic sequence, a geometric sequence, or neither. If the sequence is arithmetic find the common difference. If the sequence is geometric find the common ratio. $1 , - \frac { 3 } { 2 } , 2 , - \frac { 5 } { 2 }$

Accepted Answer

A)  arithmetic, $d = - \frac { 3 } { 2 }$ 
B)  arithmetic, $d = - \frac { 1 } { 2 }$ 
C)  geomettic, $r = - \frac { 3 } { 2 }$ 
D)  geometric, $r = - \frac { 5 } { 4 }$ 
E)  neither 
A)  arithmetic, $d = - \frac { 3 } { 2 }$ 
B)  arithmetic, $d = - \frac { 1 } { 2 }$ 
C)  geomettic, $r = - \frac { 3 } { 2 }$ 
D)  geometric, $r = - \frac { 5 } { 4 }$ 
E)  neither

Question 6

Find the $1000 ^ { \mathrm { th } }$ term of the sequence $a _ { n } = ( - 1 ) ^ { n } \frac { n + 2 } { n }$

Accepted Answer

A)  $a _ { 1000 } = - \frac { 501 } { 500 }$ 
B)  $a _ { 1000 } = \frac { 251 } { 250 }$ 
C)  $a _ { 1000 } = \frac { 126 } { 125 }$ 
D)  $a _ { 1000 } = - \frac { 126 } { 125 }$ 
E)  $a _ { 1000 } = \frac { 501 } { 500 }$ 
A)  $a _ { 1000 } = - \frac { 501 } { 500 }$ 
B)  $a _ { 1000 } = \frac { 251 } { 250 }$ 
C)  $a _ { 1000 } = \frac { 126 } { 125 }$ 
D)  $a _ { 1000 } = - \frac { 126 } { 125 }$ 
E)  $a _ { 1000 } = \frac { 501 } { 500 }$

Question 7

Find the first four terms and the $1000 ^ { \text {th } }$  term of the sequence $a _ { n } = ( - 1 ) ^ { n } \frac { n + 2 } { n }$

Accepted Answer

The answer of Find the first four terms and the...

Question 8

Find the values of x and y for which the sequence $2 , x , y , 17 , \ldots$ 
is arithmetic.

Accepted Answer

The answer of Find the values of x and y...

Question 9

A city was incorporated in 2004 with a population of 25,000. It is expected that the population will increase at a rate of 2% per year. The population n years after 2004 is given by the sequence $P _ { n } = 25000 ( 1.02 ) ^ { n }$ Find the population in 2014

Accepted Answer

A)  $26,530$ 
B)  $27,061$ 
C)  $30,475$ 
D)  $32,987$ 
E)  none of these 
A)  $26,530$ 
B)  $27,061$ 
C)  $30,475$ 
D)  $32,987$ 
E)  none of these

Question 10

Determine whether the expression is a partial sum of an arithmetic or geometric sequence. Then find the sum. $5 + 25 + 125 + \ldots + 15625$

Accepted Answer

@#LAT-DLM& , @#LAT-DLM& , so @#LAT-DLM&

Question 11

Find the first five terms of the sequence $a _ { n } = 3 \left( a _ { n - 1 } + 1 \right)$ , where $a _ { 1 } = 1$

Accepted Answer

The answer of Find the first five terms of the...

Question 12

A man gets a job with a salary of $50,000 a year. He is promised an $1800 raise each subsequent year. Find his total earnings for a 10-year period

Accepted Answer

A)  $\$ 518,000$ 
B)  $\$ 851,000$ 
C)  $\$ 1,581,000$ 
D)  $\$ 481,000$ 
E)  none of these 
A)  $\$ 518,000$ 
B)  $\$ 851,000$ 
C)  $\$ 1,581,000$ 
D)  $\$ 481,000$ 
E)  none of these

Question 13

Find the second term in the expansion of $\left( x ^ { 2 } - \frac { 1 } { x } \right) ^ { 50 }$

Accepted Answer

A)  $50 x ^ { 97 }$ 
B)  $- 47 x ^ { 47 }$ 
C)  $- 50 x ^ { 48 }$ 
D)  $50 x ^ { 49 }$ 
E)  $- 50 x ^ { 97 }$ 
A)  $50 x ^ { 97 }$ 
B)  $- 47 x ^ { 47 }$ 
C)  $- 50 x ^ { 48 }$ 
D)  $50 x ^ { 49 }$ 
E)  $- 50 x ^ { 97 }$

Question 14

Find the first four terms and the $10 ^ { \text {th } }$  term of the sequence $a _ { n } = n - 1$

Accepted Answer

The answer of Find the first four terms and the...

Question 15

Write the sum without using sigma notation. $\sum _ { n = 2 } ^ { 100 } \frac { 1 } { n - 1 }$

Accepted Answer

A)  $1 + 2 + \frac { 1 } { 3 } + \frac { 1 } { 4 } + \ldots + \frac { 1 } { 99 } + \frac { 1 } { 100 }$ 
B)  $\frac { 1 } { 1 } + \frac { 1 } { 2 } + \frac { 1 } { 3 } + \frac { 1 } { 4 } + \ldots + \frac { 1 } { 98 } + \frac { 1 } { 99 }$ 
C)  $\frac { 1 } { 1 } + \frac { 1 } { 2 } + \frac { 1 } { 3 } + \frac { 1 } { 4 } + \ldots + \frac { 1 } { 99 } + \frac { 1 } { 100 }$ 
D)  $\frac { 1 } { 1 } + \frac { 1 } { 2 } + \frac { 1 } { 3 } + \frac { 1 } { 4 } + \ldots + \frac { 1 } { 97 } + \frac { 1 } { 98 }$ 
E)  none of these 
A)  $1 + 2 + \frac { 1 } { 3 } + \frac { 1 } { 4 } + \ldots + \frac { 1 } { 99 } + \frac { 1 } { 100 }$ 
B)  $\frac { 1 } { 1 } + \frac { 1 } { 2 } + \frac { 1 } { 3 } + \frac { 1 } { 4 } + \ldots + \frac { 1 } { 98 } + \frac { 1 } { 99 }$ 
C)  $\frac { 1 } { 1 } + \frac { 1 } { 2 } + \frac { 1 } { 3 } + \frac { 1 } { 4 } + \ldots + \frac { 1 } { 99 } + \frac { 1 } { 100 }$ 
D)  $\frac { 1 } { 1 } + \frac { 1 } { 2 } + \frac { 1 } { 3 } + \frac { 1 } { 4 } + \ldots + \frac { 1 } { 97 } + \frac { 1 } { 98 }$ 
E)  none of these

Question 16

Find the first five terms of the sequence $a _ { n } = 3 \left( a _ { n - 1 } + 1 \right)$ , where $a _ { 1 } = 1$

Accepted Answer

A)  $a _ { 1 } = 1$, $a _ { 2 } = 6$, $a _ { 3 } = 21$, $a _ { 4 } = 66$, $a _ { 3 } = 201$ 
B)  $a _ { 1 } = 3$, $a _ { 2 } = 9$, $a _ { 3 } = 27$, $a _ { 4 } = 69$, $a _ { 3 } = 226$ 
C)  $a _ { 1 } = 3$, $a _ { 2 } = 12$, $a _ { 3 } = 15$, $a _ { 4 } = 18$, $a _ { 3 } = 21$ 
D)  $a _ { 1 } = 1$, $a _ { 2 } = 7$, $a _ { 3 } = 22$, $a _ { 4 } = 67$, $a _ { 3 } = 202$ 
E)  none of these 
A)  $a _ { 1 } = 1$, $a _ { 2 } = 6$, $a _ { 3 } = 21$, $a _ { 4 } = 66$, $a _ { 3 } = 201$ 
B)  $a _ { 1 } = 3$, $a _ { 2 } = 9$, $a _ { 3 } = 27$, $a _ { 4 } = 69$, $a _ { 3 } = 226$ 
C)  $a _ { 1 } = 3$, $a _ { 2 } = 12$, $a _ { 3 } = 15$, $a _ { 4 } = 18$, $a _ { 3 } = 21$ 
D)  $a _ { 1 } = 1$, $a _ { 2 } = 7$, $a _ { 3 } = 22$, $a _ { 4 } = 67$, $a _ { 3 } = 202$ 
E)  none of these

Question 17

Find the $1000 ^ { \mathrm { th } }$ term of the sequence $a _ { n } = ( - 1 ) ^ { n } \frac { n + 2 } { n }$

Accepted Answer

A)  $a _ { 1000 } = - \frac { 501 } { 500 }$ 
B)  $a _ { 1000 } = \frac { 251 } { 250 }$ 
C)  $a _ { 1000 } = \frac { 126 } { 125 }$ 
D)  $a_{1000}= - \frac { 126 } { 125 }$ 
E)  $a _ { 1000 } = \frac { 501 } { 500 }$ 
A)  $a _ { 1000 } = - \frac { 501 } { 500 }$ 
B)  $a _ { 1000 } = \frac { 251 } { 250 }$ 
C)  $a _ { 1000 } = \frac { 126 } { 125 }$ 
D)  $a_{1000}= - \frac { 126 } { 125 }$ 
E)  $a _ { 1000 } = \frac { 501 } { 500 }$

Question 18

The first term of the arithmetic sequence is $\frac {2 } { 3 }$ and the common difference is $\left( - \frac { 2 } { 3 } \right\}$Which term of this sequence is $- \frac { 20 } { 3 }$?

Accepted Answer

A)  $10 ^ { \mathrm { th} } \text { term }$ 
B)  $12 ^ { \text {th } } \text { term }$ 
C)  $13 ^ { \text {th } } \text { term }$ 
D)  $16 ^ { \mathrm { th } } \text { term }$ 
E)  $6 ^ { \mathrm { th } } \text { term }$ 
A)  $10 ^ { \mathrm { th} } \text { term }$ 
B)  $12 ^ { \text {th } } \text { term }$ 
C)  $13 ^ { \text {th } } \text { term }$ 
D)  $16 ^ { \mathrm { th } } \text { term }$ 
E)  $6 ^ { \mathrm { th } } \text { term }$

Question 19

Which term of the arithmetic sequence $\frac { 1 } { 2 } , 2 , \frac { 7 } { 2 } , \ldots$  is $23$  ?

Accepted Answer

The answer of Which term of the arithmetic sequence \(\frac...

Question 20

A ball rebounds to one-quarter the height from which it was dropped. Approximate the total vertical distance the ball travels after being dropped from $3$ ft above the ground, until it comes to rest

Accepted Answer

A)  $5 \mathrm { ft }$ 
B)  $5.25 \mathrm { ft }$ 
C)  $4.125 \mathrm { ft }$ 
D)  $3.5 \mathrm { ft }$ 
E)  $3.25 \mathrm { ft }$ 
A)  $5 \mathrm { ft }$ 
B)  $5.25 \mathrm { ft }$ 
C)  $4.125 \mathrm { ft }$ 
D)  $3.5 \mathrm { ft }$ 
E)  $3.25 \mathrm { ft }$

Determine whether the expression is a partial sum of an arithmetic or geometric sequence. Then find the sum. $5 + 25 + 125 +\dots + 3125$

Find the amount of an annuity that consists of $30$ annual payments of $\$ 500$ Each into an account that pays $7 \%$ Interest per year

Determine whether the expression is a partial sum of an arithmetic or geometric sequence. Then find the sum. $5 + 25 + 125 + \dots + 3125$

Find the first four terms of the sequence $a _ { n } = n - 2$

Find the $1000 ^ { \mathrm { th } }$ term of the sequence $a _ { n } = ( - 1 ) ^ { n } \frac { n + 2 } { n }$

Find the first four terms and the $1000 ^ { \text {th } }$ term of the sequence $a _ { n } = ( - 1 ) ^ { n } \frac { n + 2 } { n }$

Find the values of x and y for which the sequence $2 , x , y , 17 , \ldots$ is arithmetic.

A city was incorporated in 2004 with a population of 25,000. It is expected that the population will increase at a rate of 2% per year. The population n years after 2004 is given by the sequence $P _ { n } = 25000 ( 1.02 ) ^ { n }$ Find the population in 2014

Determine whether the expression is a partial sum of an arithmetic or geometric sequence. Then find the sum. $5 + 25 + 125 + \ldots + 15625$

Find the first five terms of the sequence $a _ { n } = 3 \left( a _ { n - 1 } + 1 \right)$ , where $a _ { 1 } = 1$

A man gets a job with a salary of $50,000 a year. He is promised an $1800 raise each subsequent year. Find his total earnings for a 10-year period

Find the second term in the expansion of $\left( x ^ { 2 } - \frac { 1 } { x } \right) ^ { 50 }$

Find the first four terms and the $10 ^ { \text {th } }$ term of the sequence $a _ { n } = n - 1$

Write the sum without using sigma notation. $\sum _ { n = 2 } ^ { 100 } \frac { 1 } { n - 1 }$

Find the first five terms of the sequence $a _ { n } = 3 \left( a _ { n - 1 } + 1 \right)$ , where $a _ { 1 } = 1$

Find the $1000 ^ { \mathrm { th } }$ term of the sequence $a _ { n } = ( - 1 ) ^ { n } \frac { n + 2 } { n }$

The first term of the arithmetic sequence is $\frac {2 } { 3 }$ and the common difference is $\left( - \frac { 2 } { 3 } \right\}$ Which term of this sequence is $- \frac { 20 } { 3 }$ ?

Which term of the arithmetic sequence $\frac { 1 } { 2 } , 2 , \frac { 7 } { 2 } , \ldots$ is $23$ ?

A ball rebounds to one-quarter the height from which it was dropped. Approximate the total vertical distance the ball travels after being dropped from $3$ ft above the ground, until it comes to rest

Equations and Graphs

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

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Systems of Equations and Inequalities

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Exam 13: Sequences and Series

Determine whether the expression is a partial sum of an arithmetic or geometric sequence. Then find the sum. 5+25+125+⋯+31255 + 25 + 125 +\dots + 31255+25+125+⋯+3125

Find the amount of an annuity that consists of 303030 annual payments of $500\$ 500$500 Each into an account that pays 7%7 \%7% Interest per year

Determine whether the expression is a partial sum of an arithmetic or geometric sequence. Then find the sum. 5+25+125+⋯+31255 + 25 + 125 + \dots + 31255+25+125+⋯+3125

Find the first four terms of the sequence an=n−2a _ { n } = n - 2an​=n−2

Find the 1000th1000 ^ { \mathrm { th } }1000th term of the sequence an=(−1)nn+2na _ { n } = ( - 1 ) ^ { n } \frac { n + 2 } { n }an​=(−1)nnn+2​

Find the first four terms and the 1000th 1000 ^ { \text {th } }1000th term of the sequence an=(−1)nn+2na _ { n } = ( - 1 ) ^ { n } \frac { n + 2 } { n }an​=(−1)nnn+2​

Find the values of x and y for which the sequence 2,x,y,17,…2 , x , y , 17 , \ldots2,x,y,17,… is arithmetic.

A city was incorporated in 2004 with a population of 25,000. It is expected that the population will increase at a rate of 2% per year. The population n years after 2004 is given by the sequence Pn=25000(1.02)nP _ { n } = 25000 ( 1.02 ) ^ { n }Pn​=25000(1.02)n Find the population in 2014

Determine whether the expression is a partial sum of an arithmetic or geometric sequence. Then find the sum. 5+25+125+…+156255 + 25 + 125 + \ldots + 156255+25+125+…+15625

Find the first five terms of the sequence an=3(an−1+1)a _ { n } = 3 \left( a _ { n - 1 } + 1 \right)an​=3(an−1​+1) , where a1=1a _ { 1 } = 1a1​=1

A man gets a job with a salary of $50,000 a year. He is promised an $1800 raise each subsequent year. Find his total earnings for a 10-year period

Find the second term in the expansion of (x2−1x)50\left( x ^ { 2 } - \frac { 1 } { x } \right) ^ { 50 }(x2−x1​)50

Find the first four terms and the 10th 10 ^ { \text {th } }10th term of the sequence an=n−1a _ { n } = n - 1an​=n−1

Write the sum without using sigma notation. ∑n=21001n−1\sum _ { n = 2 } ^ { 100 } \frac { 1 } { n - 1 }∑n=2100​n−11​

Find the first five terms of the sequence an=3(an−1+1)a _ { n } = 3 \left( a _ { n - 1 } + 1 \right)an​=3(an−1​+1) , where a1=1a _ { 1 } = 1a1​=1

Find the 1000th1000 ^ { \mathrm { th } }1000th term of the sequence an=(−1)nn+2na _ { n } = ( - 1 ) ^ { n } \frac { n + 2 } { n }an​=(−1)nnn+2​

The first term of the arithmetic sequence is 23\frac {2 } { 3 }32​ and the common difference is (−23}\left( - \frac { 2 } { 3 } \right\}(−32​} Which term of this sequence is −203- \frac { 20 } { 3 }−320​ ?

Which term of the arithmetic sequence 12,2,72,…\frac { 1 } { 2 } , 2 , \frac { 7 } { 2 } , \ldots21​,2,27​,… is 232323 ?

A ball rebounds to one-quarter the height from which it was dropped. Approximate the total vertical distance the ball travels after being dropped from 333 ft above the ground, until it comes to rest

Equations and Graphs

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Counting and Probability

Filters

Determine whether the expression is a partial sum of an arithmetic or geometric sequence. Then find the sum. $5 + 25 + 125 +\dots + 3125$

Find the amount of an annuity that consists of $30$ annual payments of $\$ 500$ Each into an account that pays $7 \%$ Interest per year

Determine whether the expression is a partial sum of an arithmetic or geometric sequence. Then find the sum. $5 + 25 + 125 + \dots + 3125$

Find the first four terms of the sequence $a _ { n } = n - 2$

Find the $1000 ^ { \mathrm { th } }$ term of the sequence $a _ { n } = ( - 1 ) ^ { n } \frac { n + 2 } { n }$

Find the first four terms and the $1000 ^ { \text {th } }$ term of the sequence $a _ { n } = ( - 1 ) ^ { n } \frac { n + 2 } { n }$

Find the values of x and y for which the sequence $2 , x , y , 17 , \ldots$ is arithmetic.

A city was incorporated in 2004 with a population of 25,000. It is expected that the population will increase at a rate of 2% per year. The population n years after 2004 is given by the sequence $P _ { n } = 25000 ( 1.02 ) ^ { n }$ Find the population in 2014

Determine whether the expression is a partial sum of an arithmetic or geometric sequence. Then find the sum. $5 + 25 + 125 + \ldots + 15625$

Find the first five terms of the sequence $a _ { n } = 3 \left( a _ { n - 1 } + 1 \right)$ , where $a _ { 1 } = 1$

Find the second term in the expansion of $\left( x ^ { 2 } - \frac { 1 } { x } \right) ^ { 50 }$

Find the first four terms and the $10 ^ { \text {th } }$ term of the sequence $a _ { n } = n - 1$

Write the sum without using sigma notation. $\sum _ { n = 2 } ^ { 100 } \frac { 1 } { n - 1 }$

Find the first five terms of the sequence $a _ { n } = 3 \left( a _ { n - 1 } + 1 \right)$ , where $a _ { 1 } = 1$

Find the $1000 ^ { \mathrm { th } }$ term of the sequence $a _ { n } = ( - 1 ) ^ { n } \frac { n + 2 } { n }$

The first term of the arithmetic sequence is $\frac {2 } { 3 }$ and the common difference is $\left( - \frac { 2 } { 3 } \right\}$ Which term of this sequence is $- \frac { 20 } { 3 }$ ?

Which term of the arithmetic sequence $\frac { 1 } { 2 } , 2 , \frac { 7 } { 2 } , \ldots$ is $23$ ?

A ball rebounds to one-quarter the height from which it was dropped. Approximate the total vertical distance the ball travels after being dropped from $3$ ft above the ground, until it comes to rest