Question 1

Find the sum
-$\sum_{i=2}^{5}(4 i-4)$

Accepted Answer

A)  36 
B)  24 
C)  40 
D)  32 
A)  36 
B)  24 
C)  40 
D)  32 C

Question 2

Find the total distance traveled by a ball, given its starting height and the percent of its height that it rebounds to after bouncing. Round to the nearest tenth of a foot if necessary.
-Starting height: 200 feet; rebounds $15 \%$

Accepted Answer

A)  1533.3 feet 
B)  173.9 feet 
C)  270.6 feet 
D)  235.3 feet 
A)  1533.3 feet 
B)  173.9 feet 
C)  270.6 feet 
D)  235.3 feet C

Question 3

Find the partial sum of the arithmetic sequence with the given first term and common difference  
-$\mathrm{s}_{5}, \mathrm{a}_{1}=2, \mathrm{~d}=1$

Accepted Answer

A)  20 
B)  7 
C)  2 
D)  10 
A)  20 
B)  7 
C)  2 
D)  10 A

Question 4

Find the indicated partial sum for the given sequence
-$s_{5}, 4,2,0,-2, \ldots$

Accepted Answer

A)  -6 
B)  4 
C)  20 
D)  0 
A)  -6 
B)  4 
C)  20 
D)  0

Question 5

For the given geometric sequence, find the limit of the infinite series, if it exists.
-$1,-1,1,-1, \ldots$

Accepted Answer

A)  2 
B)  - 1 
C)  1 
D)  No limit 
A)  2 
B)  - 1 
C)  1 
D)  No limit

Question 6

Solve the problem.
-The population of a town was 35,200 at the beginning of 1970 . If the population decreased 300 people per year, how many people lived in the town at the beginning of 1985 ?

Accepted Answer

A)  30,400 
B)  4500 
C)  30,700 
D)  31,000 
A)  30,400 
B)  4500 
C)  30,700 
D)  31,000

Question 7

Find the indicated partial sum for the given sequence with the given first term and general term
-$\mathrm{s}_{4}, \mathrm{a}_{1}=1, \mathrm{a}_{\mathrm{n}}=\left(\mathrm{a}_{\mathrm{n}}-1\right)^{2}+2$

Accepted Answer

A)  10 
B)  136 
C)  6 
D)  138 
A)  10 
B)  136 
C)  6 
D)  138

Question 8

Find the general term, $a_n$, of the given geometric sequence
-$6,36,216, \ldots$

Accepted Answer

A)  $a_{n}=6^{n+1}-30$ 
B)  $a_{n}=6+30(n-1)$ 
C)  $a_{n}=6^{n-1}+5$ 
D)  $a_{n}=6^{n}$ 
A)  $a_{n}=6^{n+1}-30$ 
B)  $a_{n}=6+30(n-1)$ 
C)  $a_{n}=6^{n-1}+5$ 
D)  $a_{n}=6^{n}$

Question 9

Use the formulas $\sum_{i=1}^{n} i=\frac{n(n+1)}{2}, \sum_{i=1}^{n} i^{2}=\frac{n(n+1)(2 n+1)}{6}$, and $\sum_{i=1}^{n} 
-\(\sum_{i=1}^{10}\left(2 i^{3}-5 i^{2}\right)$

Accepted Answer

A)  14,355 
B)  5280 
C)  11,625 
D)  4125 
A)  14,355 
B)  5280 
C)  11,625 
D)  4125

Question 10

Find the first five terms of the geometric sequence with the given first term and common ratio
-$\mathrm{a}_{1}=-2, \mathrm{r}=-\frac{1}{7}$

Accepted Answer

A)  $-2,-\frac{2}{7},-\frac{2}{49},-\frac{2}{343},-\frac{2}{2401}$ 
B)  $-2,14,-98,686,-4802$ 
C)  $-2,-14,-98,-686,-4802$ 
D)  $-2, \frac{2}{7},-\frac{2}{49}, \frac{2}{343},-\frac{2}{2401}$ 
A)  $-2,-\frac{2}{7},-\frac{2}{49},-\frac{2}{343},-\frac{2}{2401}$ 
B)  $-2,14,-98,686,-4802$ 
C)  $-2,-14,-98,-686,-4802$ 
D)  $-2, \frac{2}{7},-\frac{2}{49}, \frac{2}{343},-\frac{2}{2401}$

Question 11

Evaluate the given binomial coefficient
-${}_7 \mathrm{C}_{7}$

Accepted Answer

A)  0.5 
B)  1 
C)  5040 
D)  1260 
A)  0.5 
B)  1 
C)  5040 
D)  1260

Question 12

Use an infinite geometric series to rewrite the repeating decimal as a lowest-terms fraction
-$0 . \overline{5}$

Accepted Answer

A)  $\frac{5}{11}$ 
B)  $\frac{5}{7}$ 
C)  $\frac{5}{9}$ 
D)  $\frac{5}{10}$ 
A)  $\frac{5}{11}$ 
B)  $\frac{5}{7}$ 
C)  $\frac{5}{9}$ 
D)  $\frac{5}{10}$

Question 13

Write the sum using summation notation
-$0+1+2+3+4$

Accepted Answer

A)  $\sum_{i=1}^{5}(i-1)$ 
B)  $\sum_{i=1}^{4}(i-1)$ 
C)  $\sum_{i=1}^{5}(n-1)$ 
D)  $\sum_{i=1}^{5} \mathrm{i}$ 
A)  $\sum_{i=1}^{5}(i-1)$ 
B)  $\sum_{i=1}^{4}(i-1)$ 
C)  $\sum_{i=1}^{5}(n-1)$ 
D)  $\sum_{i=1}^{5} \mathrm{i}$

Question 14

Find the partial sum of the geometric sequence with the given first term and common ratio
-$\mathrm{s}_{4}, \mathrm{a}_{1}=-5, \mathrm{r}=3$

Accepted Answer

A)  -65 
B)  -40 
C)  200 
D)  -200 
A)  -65 
B)  -40 
C)  200 
D)  -200

Question 15

Find the common difference,d, of the given arithmetic sequence
-$-8,-13,-18,-23, \ldots$

Accepted Answer

A)  -10 
B)  -15 
C)  -5 
A)  -10 
B)  -15 
C)  -5

Question 16

Find the sum
-$\sum_{i=3}^{6} 3^{i}$

Accepted Answer

A)  1080 
B)  729 
C)  162 
D)  19,683 
A)  1080 
B)  729 
C)  162 
D)  19,683

Question 17

Find the common ratio, r, for the geometric sequence
-$2,6,18,54,162, \ldots$

Accepted Answer

A)  6 
B)  $1 / 3$ 
C)  81 
D)  3 
A)  6 
B)  $1 / 3$ 
C)  81 
D)  3

Question 18

Find the indicated term for the sequence.
-Find the $5^{\text {th }}$ term of the sequence whose general term is $a_{n}=4^{n}$.

Accepted Answer

A)  1024 
B)  625 
C)  256 
D)  20 
A)  1024 
B)  625 
C)  256 
D)  20

Question 19

Find the indicated partial sum for the given sequence
-$\mathrm{s} _5,-15,-18,-21,-24, \ldots$

Accepted Answer

A)  -15 
B)  -30 
C)  -105 
D)  -75 
A)  -15 
B)  -30 
C)  -105 
D)  -75

Question 20

Find the indicated partial sum for the given sequence
-$\mathrm{s}_{5},-\frac{1}{8}, \frac{1}{16},-\frac{1}{32}, \frac{1}{64}, \ldots$

Accepted Answer

A)  $-\frac{1}{128}$ 
B)  $-\frac{21}{256}$ 
C)  $-\frac{15}{256}$ 
D)  $-\frac{11}{128}$ 
A)  $-\frac{1}{128}$ 
B)  $-\frac{21}{256}$ 
C)  $-\frac{15}{256}$ 
D)  $-\frac{11}{128}$

Find the sum - $\sum_{i=2}^{5}(4 i-4)$

Find the total distance traveled by a ball, given its starting height and the percent of its height that it rebounds to after bouncing. Round to the nearest tenth of a foot if necessary. -Starting height: 200 feet; rebounds $15 \%$

Find the partial sum of the arithmetic sequence with the given first term and common difference - $\mathrm{s}_{5}, \mathrm{a}_{1}=2, \mathrm{~d}=1$

Find the indicated partial sum for the given sequence - $s_{5}, 4,2,0,-2, \ldots$

For the given geometric sequence, find the limit of the infinite series, if it exists. - $1,-1,1,-1, \ldots$

Solve the problem. -The population of a town was 35,200 at the beginning of 1970 . If the population decreased 300 people per year, how many people lived in the town at the beginning of 1985 ?

Find the indicated partial sum for the given sequence with the given first term and general term - $\mathrm{s}_{4}, \mathrm{a}_{1}=1, \mathrm{a}_{\mathrm{n}}=\left(\mathrm{a}_{\mathrm{n}}-1\right)^{2}+2$

Find the general term, $a_n$ , of the given geometric sequence - $6,36,216, \ldots$

Use the formulas $\sum_{i=1}^{n} i=\frac{n(n+1)}{2}, \sum_{i=1}^{n} i^{2}=\frac{n(n+1)(2 n+1)}{6}$ , and $\sum_{i=1}^{n} -\sum_{i=1}^{10}\left(2 i^{3}-5 i^{2}\right)$

Find the first five terms of the geometric sequence with the given first term and common ratio - $\mathrm{a}_{1}=-2, \mathrm{r}=-\frac{1}{7}$

Evaluate the given binomial coefficient - ${}_7 \mathrm{C}_{7}$

Use an infinite geometric series to rewrite the repeating decimal as a lowest-terms fraction - $0 . \overline{5}$

Write the sum using summation notation - $0+1+2+3+4$

Find the partial sum of the geometric sequence with the given first term and common ratio - $\mathrm{s}_{4}, \mathrm{a}_{1}=-5, \mathrm{r}=3$

Find the common difference,d, of the given arithmetic sequence - $-8,-13,-18,-23, \ldots$

Find the sum - $\sum_{i=3}^{6} 3^{i}$

Find the common ratio, r, for the geometric sequence - $2,6,18,54,162, \ldots$

Find the indicated term for the sequence. -Find the $5^{\text {th }}$ term of the sequence whose general term is $a_{n}=4^{n}$ .

Find the indicated partial sum for the given sequence - $\mathrm{s} _5,-15,-18,-21,-24, \ldots$

Find the indicated partial sum for the given sequence - $\mathrm{s}_{5},-\frac{1}{8}, \frac{1}{16},-\frac{1}{32}, \frac{1}{64}, \ldots$

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Filters

Exam 11: Sequences, Series, and the Binomial Theorem

Find the sum - ∑i=25(4i−4)\sum_{i=2}^{5}(4 i-4)∑i=25​(4i−4)

Find the total distance traveled by a ball, given its starting height and the percent of its height that it rebounds to after bouncing. Round to the nearest tenth of a foot if necessary. -Starting height: 200 feet; rebounds 15%15 \%15%

Find the partial sum of the arithmetic sequence with the given first term and common difference - s5,a1=2, d=1\mathrm{s}_{5}, \mathrm{a}_{1}=2, \mathrm{~d}=1s5​,a1​=2, d=1

Find the indicated partial sum for the given sequence - s5,4,2,0,−2,…s_{5}, 4,2,0,-2, \ldotss5​,4,2,0,−2,…

For the given geometric sequence, find the limit of the infinite series, if it exists. - 1,−1,1,−1,…1,-1,1,-1, \ldots1,−1,1,−1,…

Solve the problem. -The population of a town was 35,200 at the beginning of 1970 . If the population decreased 300 people per year, how many people lived in the town at the beginning of 1985 ?

Find the indicated partial sum for the given sequence with the given first term and general term - s4,a1=1,an=(an−1)2+2\mathrm{s}_{4}, \mathrm{a}_{1}=1, \mathrm{a}_{\mathrm{n}}=\left(\mathrm{a}_{\mathrm{n}}-1\right)^{2}+2s4​,a1​=1,an​=(an​−1)2+2

Find the general term, ana_nan​ , of the given geometric sequence - 6,36,216,…6,36,216, \ldots6,36,216,…

Find the first five terms of the geometric sequence with the given first term and common ratio - a1=−2,r=−17\mathrm{a}_{1}=-2, \mathrm{r}=-\frac{1}{7}a1​=−2,r=−71​

Evaluate the given binomial coefficient - 7C7{}_7 \mathrm{C}_{7}7​C7​

Use an infinite geometric series to rewrite the repeating decimal as a lowest-terms fraction - 0.5‾0 . \overline{5}0.5

Write the sum using summation notation - 0+1+2+3+40+1+2+3+40+1+2+3+4

Find the partial sum of the geometric sequence with the given first term and common ratio - s4,a1=−5,r=3\mathrm{s}_{4}, \mathrm{a}_{1}=-5, \mathrm{r}=3s4​,a1​=−5,r=3

Find the common difference,d, of the given arithmetic sequence - −8,−13,−18,−23,…-8,-13,-18,-23, \ldots−8,−13,−18,−23,…

Find the sum - ∑i=363i\sum_{i=3}^{6} 3^{i}∑i=36​3i

Find the common ratio, r, for the geometric sequence - 2,6,18,54,162,…2,6,18,54,162, \ldots2,6,18,54,162,…

Find the indicated term for the sequence. -Find the 5th 5^{\text {th }}5th term of the sequence whose general term is an=4na_{n}=4^{n}an​=4n .

Find the indicated partial sum for the given sequence - s5,−15,−18,−21,−24,…\mathrm{s} _5,-15,-18,-21,-24, \ldotss5​,−15,−18,−21,−24,…

Find the indicated partial sum for the given sequence - s5,−18,116,−132,164,…\mathrm{s}_{5},-\frac{1}{8}, \frac{1}{16},-\frac{1}{32}, \frac{1}{64}, \ldotss5​,−81​,161​,−321​,641​,…