Question 1

Find the common difference of the arithmetic sequence with the n th term $a _ { n } = 5 - 6 n$.

Accepted Answer

A)  -5 
B)  -6 
C)  6 
D)  -1 
E)  5 
A)  -5 
B)  -6 
C)  6 
D)  -1 
E)  5

Question 2

Find a formula for the n th term of the arithmetic sequence. $a _ { 5 } = 13 , a _ { 9 } = 3$

Accepted Answer

A)  $a _ { n } = - \frac { 5 n - 51 } { 2 }$ 
B)  $a _ { n } = \frac { 5 n - 51 } { 2 }$ 
C)  $a _ { n } = 23 n - 10$ 
D)  $\alpha _ { n } = 13 n + 10$ 
E)  $a _ { n } = - \frac { 5 n + 51 } { 2 }$ 
A)  $a _ { n } = - \frac { 5 n - 51 } { 2 }$ 
B)  $a _ { n } = \frac { 5 n - 51 } { 2 }$ 
C)  $a _ { n } = 23 n - 10$ 
D)  $\alpha _ { n } = 13 n + 10$ 
E)  $a _ { n } = - \frac { 5 n + 51 } { 2 }$

Question 3

Determine whether the sequence is geometric. If so, find the common ratio. $1,-\frac{7}{2}, \frac{49}{4},-\frac{343}{8}, \frac{2401}{16},..$

Accepted Answer

A)  $\frac{2}{7}$ 
B)  -$\frac{2}{7}$ 
C)  $\frac{7}{2}$ 
D)  -$\frac{7}{2}$ 
E) not geometric 
A)  $\frac{2}{7}$ 
B)  -$\frac{2}{7}$ 
C)  $\frac{7}{2}$ 
D)  -$\frac{7}{2}$ 
E) not geometric

Question 4

Find the common difference of the arithmetic sequence $34,45,56,67 , \ldots$

Accepted Answer

A)  22 
B)  11 
C)  -22 
D)  34 
E)  -11 
A)  22 
B)  11 
C)  -22 
D)  34 
E)  -11

Question 5

Find the n th partial sum of the arithmetic sequence. $300,257,214,171,128 \ldots , n = 9$

Accepted Answer

A)  1926 
B)  2304 
C)  -198 
D)  958.5 
E)  1152 
A)  1926 
B)  2304 
C)  -198 
D)  958.5 
E)  1152

Question 6

Use the Binomial Theorem to expand the expression $( x + 3 ) ^ { 6 }$ .

Accepted Answer

A)  $x ^ { 6 } + 729$ 
B)  $x ^ { 6 } + 3$ 
C)  $x ^ { 6 } + 3 x ^ { 5 } + 9 x ^ { 4 } + 27 x ^ { 3 } + 81 x ^ { 2 } + 243 x + 729$ 
D)  $x ^ { 6 } + 6 x ^ { 5 } + 15 x ^ { 4 } + 20 x ^ { 3 } + 15 x ^ { 2 } + 6 x + 729$ 
E)  $x ^ { 6 } + 18 x ^ { 5 } + 135 x ^ { 4 } + 540 x ^ { 3 } + 1215 x ^ { 2 } + 1458 x + 729$ 
A)  $x ^ { 6 } + 729$ 
B)  $x ^ { 6 } + 3$ 
C)  $x ^ { 6 } + 3 x ^ { 5 } + 9 x ^ { 4 } + 27 x ^ { 3 } + 81 x ^ { 2 } + 243 x + 729$ 
D)  $x ^ { 6 } + 6 x ^ { 5 } + 15 x ^ { 4 } + 20 x ^ { 3 } + 15 x ^ { 2 } + 6 x + 729$ 
E)  $x ^ { 6 } + 18 x ^ { 5 } + 135 x ^ { 4 } + 540 x ^ { 3 } + 1215 x ^ { 2 } + 1458 x + 729$

Question 7

Find $S _ { 1 } , S _ { 2 }$ and $S _ { 6 }$ for $a _ { n } = 8 n + 9$ .

Accepted Answer

A)  $S _ { 1 } = 17 ; S _ { 2 } = 34 ; S _ { 6 } = 102$ 
B)  $S _ { 1 } = 17 ; S _ { 2 } = 25 ; S _ { 6 } = 57$ 
C)  $S _ { 1 } = 17 ; S _ { 2 } = 25 ; S _ { 6 } = 177$ 
D)  $S _ { 1 } = 17 ; S _ { 2 } = 33 ; S _ { 6 } = 177$ 
E)  $S _ { 1 } = 17 ; S _ { 2 } = 42 ; S _ { 6 } = 222$ 
A)  $S _ { 1 } = 17 ; S _ { 2 } = 34 ; S _ { 6 } = 102$ 
B)  $S _ { 1 } = 17 ; S _ { 2 } = 25 ; S _ { 6 } = 57$ 
C)  $S _ { 1 } = 17 ; S _ { 2 } = 25 ; S _ { 6 } = 177$ 
D)  $S _ { 1 } = 17 ; S _ { 2 } = 33 ; S _ { 6 } = 177$ 
E)  $S _ { 1 } = 17 ; S _ { 2 } = 42 ; S _ { 6 } = 222$

Question 8

Find the n th partial sum of the arithmetic sequence. $a _ { 1 } = 0.8 , a _ { 5 } = 2.8 , \ldots , n = 13$

Accepted Answer

A)  52.65 
B)  92.30 
C)  105.30 
D)  46.15 
E)  49.40 
A)  52.65 
B)  92.30 
C)  105.30 
D)  46.15 
E)  49.40

Question 9

Write the first five terms of the sequence $\left( - \frac { 1 } { 4 } \right) ^ { n + 2 }$ . Assume that n begins with 1.

Accepted Answer

A)  $a _ { 1 } = - \frac { 1 } { 64 } , a _ { 2 } = \frac { 1 } { 256 } , a _ { 3 } = - \frac { 1 } { 1024 } , a _ { 4 } = \frac { 1 } { 4096 } , a _ { 5 } = - \frac { 1 } { 16384 }$ 
B)  $a _ { 1 } = \frac { 1 } { 16 } , a _ { 2 } = \frac { 1 } { 64 } , a _ { 3 } = \frac { 1 } { 256 } , a _ { 4 } = \frac { 1 } { 1024 } , a _ { 5 } = \frac { 1 } { 4096 }$ 
C)  $a _ { 1 } = - \frac { 1 } { 16 } , a _ { 2 } = \frac { 1 } { 64 } , a _ { 3 } = - \frac { 1 } { 256 } , a _ { 4 } = \frac { 1 } { 1024 } , a _ { 5 } = - \frac { 1 } { 4096 }$ 
D)  $a _ { 1 } = \frac { 1 } { 16 } , a _ { 2 } = - \frac { 1 } { 64 } , a _ { 3 } = \frac { 1 } { 256 } , a _ { 4 } = - \frac { 1 } { 1024 } , a _ { 5 } = \frac { 1 } { 4096 }$ 
E)  $a _ { 1 } = \frac { 1 } { 64 } , a _ { 2 } = \frac { 1 } { 256 } , a _ { 3 } = \frac { 1 } { 1024 } , a _ { 4 } = \frac { 1 } { 4096 } , a _ { 5 } = \frac { 1 } { 16384 }$ 
A)  $a _ { 1 } = - \frac { 1 } { 64 } , a _ { 2 } = \frac { 1 } { 256 } , a _ { 3 } = - \frac { 1 } { 1024 } , a _ { 4 } = \frac { 1 } { 4096 } , a _ { 5 } = - \frac { 1 } { 16384 }$ 
B)  $a _ { 1 } = \frac { 1 } { 16 } , a _ { 2 } = \frac { 1 } { 64 } , a _ { 3 } = \frac { 1 } { 256 } , a _ { 4 } = \frac { 1 } { 1024 } , a _ { 5 } = \frac { 1 } { 4096 }$ 
C)  $a _ { 1 } = - \frac { 1 } { 16 } , a _ { 2 } = \frac { 1 } { 64 } , a _ { 3 } = - \frac { 1 } { 256 } , a _ { 4 } = \frac { 1 } { 1024 } , a _ { 5 } = - \frac { 1 } { 4096 }$ 
D)  $a _ { 1 } = \frac { 1 } { 16 } , a _ { 2 } = - \frac { 1 } { 64 } , a _ { 3 } = \frac { 1 } { 256 } , a _ { 4 } = - \frac { 1 } { 1024 } , a _ { 5 } = \frac { 1 } { 4096 }$ 
E)  $a _ { 1 } = \frac { 1 } { 64 } , a _ { 2 } = \frac { 1 } { 256 } , a _ { 3 } = \frac { 1 } { 1024 } , a _ { 4 } = \frac { 1 } { 4096 } , a _ { 5 } = \frac { 1 } { 16384 }$

Question 10

Determine whether the sequence is arithmetic. If so, find the common difference. $\ln 4 , \ln 8 , \ln 12 , \ln 16 , \ln 20 , \ldots$

Accepted Answer

A)  8 
B)  4 
C)  $\ln 8$ 
D)  $\ln 4$ 
E) The sequence is not arithmetic. 
A)  8 
B)  4 
C)  $\ln 8$ 
D)  $\ln 4$ 
E) The sequence is not arithmetic.

Question 11

Find a formula for the n th term of the arithmetic sequence. $a _ { 1 } = 11 , d = 4$

Accepted Answer

A)  $\alpha _ { n } = 4 n + 11$ 
B)  $a _ { n } = 4 n + 15$ 
C)  $a _ { n } = 4 n + 7$ 
D)  $a _ { n } = \frac { n } { 2 } ( 11 + 4 n )$ 
E)  $a _ { n } = \frac { n } { 2 } ( 11 + 4 ( n - 1 ) )$ 
A)  $\alpha _ { n } = 4 n + 11$ 
B)  $a _ { n } = 4 n + 15$ 
C)  $a _ { n } = 4 n + 7$ 
D)  $a _ { n } = \frac { n } { 2 } ( 11 + 4 n )$ 
E)  $a _ { n } = \frac { n } { 2 } ( 11 + 4 ( n - 1 ) )$

Question 12

Determine whether the sequence is geometric. If so, find the common ratio. $9,15,21,27, \ldots$

Accepted Answer

A) 9 
B) 15 
C)  $\frac{5}{2}$ 
D) 6 
E) not geometric 
A) 9 
B) 15 
C)  $\frac{5}{2}$ 
D) 6 
E) not geometric

Question 13

Write an expression for the n th term of the sequence $2,5,10,17,26,....$ Assume that n begins with 1.

Accepted Answer

A)  $a _ { n } = n + 4$ 
B)  $a _ { n } = n ^ { 2 } + 1$ 
C)  $a _ { n } = n ^ { 3 } + 1$ 
D)  $a _ { n } = n ^ { 3 } - 2$ 
E)  $a _ { n } = n ^ { 2 } - 2$ 
A)  $a _ { n } = n + 4$ 
B)  $a _ { n } = n ^ { 2 } + 1$ 
C)  $a _ { n } = n ^ { 3 } + 1$ 
D)  $a _ { n } = n ^ { 3 } - 2$ 
E)  $a _ { n } = n ^ { 2 } - 2$

Question 14

A ball is dropped from a height of 10 feet. Each time it drops h feet, it rebounds 0.79 h feet. Find the total distance traveled by the ball. Round your answer to two decimal places.

Accepted Answer

A) 75.24 
B) 37.62 
C) 47.62 
D) 85.24 
E) 22.66 
A) 75.24 
B) 37.62 
C) 47.62 
D) 85.24 
E) 22.66

Question 15

Find the partial sum $\sum _ { j = 1 } ^ { 3 } \frac { ( - 1 ) ^ { j } } { j ^ { 3 } }$ .

Accepted Answer

A)  $- \frac { 235 } { 216 }$ 
B)  $\frac { 65 } { 216 }$ 
C)  $- \frac { 65 } { 216 }$ 
D)  $- \frac { 197 } { 216 }$ 
E)  $\frac { 197 } { 216 }$ 
A)  $- \frac { 235 } { 216 }$ 
B)  $\frac { 65 } { 216 }$ 
C)  $- \frac { 65 } { 216 }$ 
D)  $- \frac { 197 } { 216 }$ 
E)  $\frac { 197 } { 216 }$

Question 16

A jogger decides to take a jog of $12$ miles. The first two miles take the jogger $8$ minutes and $10$ minutes respectively to complete each mile. The jogger estimates that this pattern will continue for $12$ miles. Estimate the time required to jog $12$ miles.

Accepted Answer

A)  $240$ minutes 
B)  $228$ minutes 
C)  $180$ minutes 
D)  $168$ minutes 
E)  $264$ minutes 
A)  $240$ minutes 
B)  $228$ minutes 
C)  $180$ minutes 
D)  $168$ minutes 
E)  $264$ minutes

Question 17

Find the n th partial sum of the geometric sequence. $5,15,45,135,405, \ldots, \quad n=7$

Accepted Answer

A) 1,820 
B) 5,465 
C) 200 
D) 5,514 
E) 5,808 
A) 1,820 
B) 5,465 
C) 200 
D) 5,514 
E) 5,808

Question 18

Find the n th partial sum of the arithmetic sequence. $9,16,23,30,37 , \ldots , n = 10$

Accepted Answer

A)  440 
B)  790 
C)  405 
D)  395 
E)  880 
A)  440 
B)  790 
C)  405 
D)  395 
E)  880

Find the common difference of the arithmetic sequence with the n th term $a _ { n } = 5 - 6 n$ .

Find a formula for the n th term of the arithmetic sequence. $a _ { 5 } = 13 , a _ { 9 } = 3$

Determine whether the sequence is geometric. If so, find the common ratio. $1,-\frac{7}{2}, \frac{49}{4},-\frac{343}{8}, \frac{2401}{16},..$

Find the common difference of the arithmetic sequence $34,45,56,67 , \ldots$

Find the n th partial sum of the arithmetic sequence. $300,257,214,171,128 \ldots , n = 9$

Use the Binomial Theorem to expand the expression $( x + 3 ) ^ { 6 }$ .

Find $S _ { 1 } , S _ { 2 }$ and $S _ { 6 }$ for $a _ { n } = 8 n + 9$ .

Find the n th partial sum of the arithmetic sequence. $a _ { 1 } = 0.8 , a _ { 5 } = 2.8 , \ldots , n = 13$

Write the first five terms of the sequence $\left( - \frac { 1 } { 4 } \right) ^ { n + 2 }$ . Assume that n begins with 1.

Determine whether the sequence is arithmetic. If so, find the common difference. $\ln 4 , \ln 8 , \ln 12 , \ln 16 , \ln 20 , \ldots$

Find a formula for the n th term of the arithmetic sequence. $a _ { 1 } = 11 , d = 4$

Determine whether the sequence is geometric. If so, find the common ratio. $9,15,21,27, \ldots$

Write an expression for the n th term of the sequence $2,5,10,17,26,....$ Assume that n begins with 1.

A ball is dropped from a height of 10 feet. Each time it drops h feet, it rebounds 0.79 h feet. Find the total distance traveled by the ball. Round your answer to two decimal places.

Find the partial sum $\sum _ { j = 1 } ^ { 3 } \frac { ( - 1 ) ^ { j } } { j ^ { 3 } }$ .

A jogger decides to take a jog of $12$ miles. The first two miles take the jogger $8$ minutes and $10$ minutes respectively to complete each mile. The jogger estimates that this pattern will continue for $12$ miles. Estimate the time required to jog $12$ miles.

Find the n th partial sum of the geometric sequence. $5,15,45,135,405, \ldots, \quad n=7$

Find the n th partial sum of the arithmetic sequence. $9,16,23,30,37 , \ldots , n = 10$

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

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Rational Expressions, Equations, and Functions

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Exam 11: Sequences, Series, and the Binomial Theorem

Find the common difference of the arithmetic sequence with the n th term an=5−6na _ { n } = 5 - 6 nan​=5−6n .

Find a formula for the n th term of the arithmetic sequence. a5=13,a9=3a _ { 5 } = 13 , a _ { 9 } = 3a5​=13,a9​=3

Determine whether the sequence is geometric. If so, find the common ratio. 1,−72,494,−3438,240116,..1,-\frac{7}{2}, \frac{49}{4},-\frac{343}{8}, \frac{2401}{16},..1,−27​,449​,−8343​,162401​,..

Find the common difference of the arithmetic sequence 34,45,56,67,…34,45,56,67 , \ldots34,45,56,67,…

Find the n th partial sum of the arithmetic sequence. 300,257,214,171,128…,n=9300,257,214,171,128 \ldots , n = 9300,257,214,171,128…,n=9

Use the Binomial Theorem to expand the expression (x+3)6( x + 3 ) ^ { 6 }(x+3)6 .

Find S1,S2S _ { 1 } , S _ { 2 }S1​,S2​ and S6S _ { 6 }S6​ for an=8n+9a _ { n } = 8 n + 9an​=8n+9 .

Find the n th partial sum of the arithmetic sequence. a1=0.8,a5=2.8,…,n=13a _ { 1 } = 0.8 , a _ { 5 } = 2.8 , \ldots , n = 13a1​=0.8,a5​=2.8,…,n=13

Write the first five terms of the sequence (−14)n+2\left( - \frac { 1 } { 4 } \right) ^ { n + 2 }(−41​)n+2 . Assume that n begins with 1.

Determine whether the sequence is arithmetic. If so, find the common difference. ln⁡4,ln⁡8,ln⁡12,ln⁡16,ln⁡20,…\ln 4 , \ln 8 , \ln 12 , \ln 16 , \ln 20 , \ldotsln4,ln8,ln12,ln16,ln20,…

Find a formula for the n th term of the arithmetic sequence. a1=11,d=4a _ { 1 } = 11 , d = 4a1​=11,d=4

Determine whether the sequence is geometric. If so, find the common ratio. 9,15,21,27,…9,15,21,27, \ldots9,15,21,27,…

Write an expression for the n th term of the sequence 2,5,10,17,26,....2,5,10,17,26,....2,5,10,17,26,.... Assume that n begins with 1.

A ball is dropped from a height of 10 feet. Each time it drops h feet, it rebounds 0.79 h feet. Find the total distance traveled by the ball. Round your answer to two decimal places.

Find the partial sum ∑j=13(−1)jj3\sum _ { j = 1 } ^ { 3 } \frac { ( - 1 ) ^ { j } } { j ^ { 3 } }∑j=13​j3(−1)j​ .

A jogger decides to take a jog of 121212 miles. The first two miles take the jogger 888 minutes and 101010 minutes respectively to complete each mile. The jogger estimates that this pattern will continue for 121212 miles. Estimate the time required to jog 121212 miles.

Find the n th partial sum of the geometric sequence. 5,15,45,135,405,…,n=75,15,45,135,405, \ldots, \quad n=75,15,45,135,405,…,n=7

Find the n th partial sum of the arithmetic sequence. 9,16,23,30,37,…,n=109,16,23,30,37 , \ldots , n = 109,16,23,30,37,…,n=10

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Filters

Find the common difference of the arithmetic sequence with the n th term $a _ { n } = 5 - 6 n$ .

Find a formula for the n th term of the arithmetic sequence. $a _ { 5 } = 13 , a _ { 9 } = 3$

Determine whether the sequence is geometric. If so, find the common ratio. $1,-\frac{7}{2}, \frac{49}{4},-\frac{343}{8}, \frac{2401}{16},..$

Find the common difference of the arithmetic sequence $34,45,56,67 , \ldots$

Find the n th partial sum of the arithmetic sequence. $300,257,214,171,128 \ldots , n = 9$

Use the Binomial Theorem to expand the expression $( x + 3 ) ^ { 6 }$ .

Find $S _ { 1 } , S _ { 2 }$ and $S _ { 6 }$ for $a _ { n } = 8 n + 9$ .

Find the n th partial sum of the arithmetic sequence. $a _ { 1 } = 0.8 , a _ { 5 } = 2.8 , \ldots , n = 13$

Write the first five terms of the sequence $\left( - \frac { 1 } { 4 } \right) ^ { n + 2 }$ . Assume that n begins with 1.

Determine whether the sequence is arithmetic. If so, find the common difference. $\ln 4 , \ln 8 , \ln 12 , \ln 16 , \ln 20 , \ldots$

Find a formula for the n th term of the arithmetic sequence. $a _ { 1 } = 11 , d = 4$

Determine whether the sequence is geometric. If so, find the common ratio. $9,15,21,27, \ldots$

Write an expression for the n th term of the sequence $2,5,10,17,26,....$ Assume that n begins with 1.

Find the partial sum $\sum _ { j = 1 } ^ { 3 } \frac { ( - 1 ) ^ { j } } { j ^ { 3 } }$ .

A jogger decides to take a jog of $12$ miles. The first two miles take the jogger $8$ minutes and $10$ minutes respectively to complete each mile. The jogger estimates that this pattern will continue for $12$ miles. Estimate the time required to jog $12$ miles.

Find the n th partial sum of the geometric sequence. $5,15,45,135,405, \ldots, \quad n=7$

Find the n th partial sum of the arithmetic sequence. $9,16,23,30,37 , \ldots , n = 10$