Question 1

Find the first five terms of the geometric sequence with the given first term and common ratio
-$\mathrm{a}_{1}=8, \mathrm{r}=-6$

Accepted Answer

A)  $-48,288,-1728,10,368,-62,208$ 
B)  $8,2,-12,-10,-16$ 
C)  $8,-48,288,-1728,10,368$ 
D)  $8,48,288,1728,10,368$ 
A)  $-48,288,-1728,10,368,-62,208$ 
B)  $8,2,-12,-10,-16$ 
C)  $8,-48,288,-1728,10,368$ 
D)  $8,48,288,1728,10,368$

Question 2

Find the first five terms of the arithmetic sequence with the given first term and common difference
-$\mathrm{a}_{1}=12, \mathrm{~d}=-2$

Accepted Answer

A)  $16,13,10,7,4$ 
B)  $12,10,8,6,4$ 
C)  $0,12,10,8,6$ 
D)  $-12,-10,-8,-6,-4$ 
A)  $16,13,10,7,4$ 
B)  $12,10,8,6,4$ 
C)  $0,12,10,8,6$ 
D)  $-12,-10,-8,-6,-4$

Question 3

Find the indicated term for the sequence.
-Find the $12^{\text {th }}$ term of the sequence whose general term is $a_{n}=(3 n-8)(5 n+5)$.

Accepted Answer

A)  1500 
B)  1820 
C)  2170 
D)  1210 
A)  1500 
B)  1820 
C)  2170 
D)  1210

Question 4

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 $\sum_{i=1}^{n} i^{3}=\left[\frac{n(n+1)}{2}\right]^{2}$ to find the sum.
-Find the sum of the first 32 squared positive integers.

Accepted Answer

A)  5720 
B)  278,784 
C)  528 
D)  11,440 
A)  5720 
B)  278,784 
C)  528 
D)  11,440

Question 5

Find the first four terms of the given sequence.
-$a_{1}=5, a_{n}=\frac{(-1)^{n-1}}{a_{n}-1}$

Accepted Answer

A)  - $5, \frac{1}{2},-\frac{1}{3}, \frac{1}{4}$ 
B)  $5,-\frac{1}{5},-5, \frac{1}{5}$ 
C)  $5,-\frac{1}{5}, 5,-\frac{1}{5}$ 
D)  $5,-\frac{1}{5}, \frac{1}{25},-\frac{1}{125}$ 
A)  - $5, \frac{1}{2},-\frac{1}{3}, \frac{1}{4}$ 
B)  $5,-\frac{1}{5},-5, \frac{1}{5}$ 
C)  $5,-\frac{1}{5}, 5,-\frac{1}{5}$ 
D)  $5,-\frac{1}{5}, \frac{1}{25},-\frac{1}{125}$

Question 6

Find the partial sum of the geometric sequence with the given first term and common ratio
-$s_{8}, a_{1}=-5, r=3$

Accepted Answer

A)  $-16,363$ 
B)  $-16,400$ 
C)  $-16,420$ 
D)  $-16,398$ 
A)  $-16,363$ 
B)  $-16,400$ 
C)  $-16,420$ 
D)  $-16,398$

Question 7

Find the common ratio, r, for the geometric sequence
-$64,-16,4,-1, \ldots$

Accepted Answer

A)  $-\frac{1}{5}$ 
B)  $\frac{1}{4}$ 
C)  -4 
D)  $-\frac{1}{4}$ 
A)  $-\frac{1}{5}$ 
B)  $\frac{1}{4}$ 
C)  -4 
D)  $-\frac{1}{4}$

Question 8

Find the indicated partial sum for the given sequence
-$s 4,81,-243,729,-2187, \ldots$

Accepted Answer

A)  4941 
B)  -2187 
C)  -1134 
D)  - 1620 
A)  4941 
B)  -2187 
C)  -1134 
D)  - 1620

Question 9

Find the first four terms of the given sequence.
-$a_{1}=3, a_{n}=a_{n}-1+8$

Accepted Answer

A)  $11,19,27,35$ 
B)  3, 11, 19, 27 
C)  $3,8,16,24$ 
D)  $0,8,16,24$ 
A)  $11,19,27,35$ 
B)  3, 11, 19, 27 
C)  $3,8,16,24$ 
D)  $0,8,16,24$

Question 10

Find the indicated partial sum for the given geometric sequence
-$\mathrm{s} 5,-32,64,-128,256, \ldots$

Accepted Answer

A)  672 
B)  -352 
C)  -512 
D)  - 480 
A)  672 
B)  -352 
C)  -512 
D)  - 480

Question 11

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 $\sum_{i=1}^{n} i^{3}=\left[\frac{n(n+1)}{2}\right]^{2}$ to find the sum.
-Find the sum of the first 275 positive integers.

Accepted Answer

A)  $6,970,150$ 
B)  75,900 
C)  37,950 
D)  $3,485,075$ 
A)  $6,970,150$ 
B)  75,900 
C)  37,950 
D)  $3,485,075$

Question 12

Find the common difference,d, of the given arithmetic sequence
-$5,9,13,17, \ldots$

Accepted Answer

A)  4 
B)  -4 
C)  12 
A)  4 
B)  -4 
C)  12

Question 13

Expand using the binomial theorem
-$(x-3)^{5}$

Accepted Answer

A)  $x^{5}-15 x^{4}+180 x^{3}-540 x^{2}+405 x-3$ 
B)  $x^{5}-15 x^{4}+180 x^{3}-540 x^{2}+405 x-243$ 
C)  $x^{5}-15 x^{4}+90 x^{3}-270 x^{2}+405 x-3$ 
D)  $x^{5}-15 x^{4}+90 x^{3}-270 x^{2}+405 x-243$ 
A)  $x^{5}-15 x^{4}+180 x^{3}-540 x^{2}+405 x-3$ 
B)  $x^{5}-15 x^{4}+180 x^{3}-540 x^{2}+405 x-243$ 
C)  $x^{5}-15 x^{4}+90 x^{3}-270 x^{2}+405 x-3$ 
D)  $x^{5}-15 x^{4}+90 x^{3}-270 x^{2}+405 x-243$

Question 14

For the given geometric sequence, find the limit of the infinite series, if it exists.
-$\frac{3}{2} \cdot\left(\frac{1}{2}\right)^{n-1}$

Accepted Answer

A)  3 
B)  No limit 
C)  $\frac{3}{2}$ 
D)  1 
A)  3 
B)  No limit 
C)  $\frac{3}{2}$ 
D)  1

Question 15

Find the indicated partial sum for the sequence with the given general term
-$\mathrm{s}_{6}, \mathrm{a}_{\mathrm{n}}=-5 \mathrm{n}-8$

Accepted Answer

A)  -13 
B)  -153 
C)  -78 
D)  - 38 
A)  -13 
B)  -153 
C)  -78 
D)  - 38

Question 16

Find the partial sum of the geometric sequence with the given first term and common ratio
-$\mathrm{s}_{5}, \mathrm{a}_{1}=\frac{3}{2}, \mathrm{r}=\frac{1}{2}$

Accepted Answer

A)  93 
B)  $\frac{93}{32}$ 
C)  $\frac{1}{32}$ 
D)  $\frac{1}{4}$ 
A)  93 
B)  $\frac{93}{32}$ 
C)  $\frac{1}{32}$ 
D)  $\frac{1}{4}$

Question 17

Examine the differences for the sequence, and determine the type of expression
-$8,5,2,-1,-4$

Accepted Answer

A)  quadratic 
B)  linear 
C)  cubic 
A)  quadratic 
B)  linear 
C)  cubic

Question 18

Simplify.
-$\frac{7 !}{5 !}$

Accepted Answer

A)  42 
B)  $\frac{1}{2 !}$ 
C)  $\frac{1}{42}$ 
D)  2 ! 
A)  42 
B)  $\frac{1}{2 !}$ 
C)  $\frac{1}{42}$ 
D)  2 !

Question 19

Find the indicated term.
-Find the 15th term of the arithmetic sequenœe - 4, - 7, - 10, ...

Accepted Answer

A)  -46 
B)  -42 
C)  -49 
D)  38 
A)  -46 
B)  -42 
C)  -49 
D)  38

Question 20

Find the partial sum of the geometric sequence with the given first term and common ratio
-$\mathrm{s}_{12}, \mathrm{a}_{1}=\frac{1}{2}, \mathrm{r}=-3$

Accepted Answer

A)  -66431 
B)  - 66433 
C)  -66430 
D)  $-\frac{132853}{2}$ 
A)  -66431 
B)  - 66433 
C)  -66430 
D)  $-\frac{132853}{2}$

Find the first five terms of the geometric sequence with the given first term and common ratio - $\mathrm{a}_{1}=8, \mathrm{r}=-6$

Find the first five terms of the arithmetic sequence with the given first term and common difference - $\mathrm{a}_{1}=12, \mathrm{~d}=-2$

Find the indicated term for the sequence. -Find the $12^{\text {th }}$ term of the sequence whose general term is $a_{n}=(3 n-8)(5 n+5)$ .

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 $\sum_{i=1}^{n} i^{3}=\left[\frac{n(n+1)}{2}\right]^{2}$ to find the sum. -Find the sum of the first 32 squared positive integers.

Find the first four terms of the given sequence. - $a_{1}=5, a_{n}=\frac{(-1)^{n-1}}{a_{n}-1}$

Find the partial sum of the geometric sequence with the given first term and common ratio - $s_{8}, a_{1}=-5, r=3$

Find the common ratio, r, for the geometric sequence - $64,-16,4,-1, \ldots$

Find the indicated partial sum for the given sequence - $s 4,81,-243,729,-2187, \ldots$

Find the first four terms of the given sequence. - $a_{1}=3, a_{n}=a_{n}-1+8$

Find the indicated partial sum for the given geometric sequence - $\mathrm{s} 5,-32,64,-128,256, \ldots$

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 $\sum_{i=1}^{n} i^{3}=\left[\frac{n(n+1)}{2}\right]^{2}$ to find the sum. -Find the sum of the first 275 positive integers.

Find the common difference,d, of the given arithmetic sequence - $5,9,13,17, \ldots$

Expand using the binomial theorem - $(x-3)^{5}$

For the given geometric sequence, find the limit of the infinite series, if it exists. - $\frac{3}{2} \cdot\left(\frac{1}{2}\right)^{n-1}$

Find the indicated partial sum for the sequence with the given general term - $\mathrm{s}_{6}, \mathrm{a}_{\mathrm{n}}=-5 \mathrm{n}-8$

Find the partial sum of the geometric sequence with the given first term and common ratio - $\mathrm{s}_{5}, \mathrm{a}_{1}=\frac{3}{2}, \mathrm{r}=\frac{1}{2}$

Examine the differences for the sequence, and determine the type of expression - $8,5,2,-1,-4$

Simplify. - $\frac{7 !}{5 !}$

Find the indicated term. -Find the 15th term of the arithmetic sequenœe - 4, - 7, - 10, ...

Find the partial sum of the geometric sequence with the given first term and common ratio - $\mathrm{s}_{12}, \mathrm{a}_{1}=\frac{1}{2}, \mathrm{r}=-3$

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 first five terms of the geometric sequence with the given first term and common ratio - a1=8,r=−6\mathrm{a}_{1}=8, \mathrm{r}=-6a1​=8,r=−6

Find the first five terms of the arithmetic sequence with the given first term and common difference - a1=12, d=−2\mathrm{a}_{1}=12, \mathrm{~d}=-2a1​=12, d=−2

Find the indicated term for the sequence. -Find the 12th 12^{\text {th }}12th term of the sequence whose general term is an=(3n−8)(5n+5)a_{n}=(3 n-8)(5 n+5)an​=(3n−8)(5n+5) .

Find the first four terms of the given sequence. - a1=5,an=(−1)n−1an−1a_{1}=5, a_{n}=\frac{(-1)^{n-1}}{a_{n}-1}a1​=5,an​=an​−1(−1)n−1​

Find the partial sum of the geometric sequence with the given first term and common ratio - s8,a1=−5,r=3s_{8}, a_{1}=-5, r=3s8​,a1​=−5,r=3

Find the common ratio, r, for the geometric sequence - 64,−16,4,−1,…64,-16,4,-1, \ldots64,−16,4,−1,…

Find the indicated partial sum for the given sequence - s4,81,−243,729,−2187,…s 4,81,-243,729,-2187, \ldotss4,81,−243,729,−2187,…

Find the first four terms of the given sequence. - a1=3,an=an−1+8a_{1}=3, a_{n}=a_{n}-1+8a1​=3,an​=an​−1+8

Find the indicated partial sum for the given geometric sequence - s5,−32,64,−128,256,…\mathrm{s} 5,-32,64,-128,256, \ldotss5,−32,64,−128,256,…

Find the common difference,d, of the given arithmetic sequence - 5,9,13,17,…5,9,13,17, \ldots5,9,13,17,…

Expand using the binomial theorem - (x−3)5(x-3)^{5}(x−3)5

For the given geometric sequence, find the limit of the infinite series, if it exists. - 32⋅(12)n−1\frac{3}{2} \cdot\left(\frac{1}{2}\right)^{n-1}23​⋅(21​)n−1

Find the indicated partial sum for the sequence with the given general term - s6,an=−5n−8\mathrm{s}_{6}, \mathrm{a}_{\mathrm{n}}=-5 \mathrm{n}-8s6​,an​=−5n−8

Find the partial sum of the geometric sequence with the given first term and common ratio - s5,a1=32,r=12\mathrm{s}_{5}, \mathrm{a}_{1}=\frac{3}{2}, \mathrm{r}=\frac{1}{2}s5​,a1​=23​,r=21​

Examine the differences for the sequence, and determine the type of expression - 8,5,2,−1,−48,5,2,-1,-48,5,2,−1,−4

Simplify. - 7!5!\frac{7 !}{5 !}5!7!​