Question 1

Use an infinite geometric series to rewrite the repeating decimal as a lowest-terms fraction
-$0 . \overline{3825}$

Accepted Answer

A)  $\frac{435}{1111}$ 
B)  $\frac{425}{1313}$ 
C)  $\frac{435}{1313}$ 
D)  $\frac{425}{1111}$ 
A)  $\frac{435}{1111}$ 
B)  $\frac{425}{1313}$ 
C)  $\frac{435}{1313}$ 
D)  $\frac{425}{1111}$

Question 2

Find the common difference,d, of the given arithmetic sequence
-$4,6,8,10, \ldots$

Accepted Answer

A)  4 
B)  1.5 
C)  2 
A)  4 
B)  1.5 
C)  2

Question 3

Find the general term $a_n$ of the given sequence
-$3,15,27,39,51, \ldots$

Accepted Answer

A)  $a_{n}=9 n-12$ 
B)  $a_{n}=12 n-3$ 
C)  $a_{n}=3(4 n-3)$ 
D)  $a_{n}=3(12)^{n-1}$ 
A)  $a_{n}=9 n-12$ 
B)  $a_{n}=12 n-3$ 
C)  $a_{n}=3(4 n-3)$ 
D)  $a_{n}=3(12)^{n-1}$

Question 4

Find the partial sum of the geometric sequence with the given first term and common ratio
-$\mathrm{s}_{13}, \mathrm{a}_{1}=8, \mathrm{r}=2$

Accepted Answer

A)  65,565 
B)  65,528 
C)  65,530 
D)  65,508 
A)  65,565 
B)  65,528 
C)  65,530 
D)  65,508

Question 5

Find the indicated partial sum for the given sequence
-$\mathrm{s}_{4},-12,-10,-8,-6, \ldots$

Accepted Answer

A)  -36 
B)  -4 
C)  -12 
D)  -48 
A)  -36 
B)  -4 
C)  -12 
D)  -48

Question 6

For the given geometric sequence, find the limit of the infinite series, if it exists.
-$-10,-5,-\frac{5}{2},-\frac{5}{4}, \ldots$

Accepted Answer

A)  -20 
B)  $-\frac{35}{2}$ 
C)  10 
D)  - 10 
A)  -20 
B)  $-\frac{35}{2}$ 
C)  10 
D)  - 10

Question 7

Write the sum using summation notation
-$0+2+6+12+20$

Accepted Answer

A)  $\sum_{i=1}^{5}\left(i^{2}+\mathrm{i}\right)$ 
B)  $\sum_{i=1}^{5}\left(i^{2}+i-2\right)$ 
C)  $\sum_{i=1}^{5}\left(i^{2}-i\right)$ 
D)  $\sum_{i=1}^{5}(2 i-2)$ 
A)  $\sum_{i=1}^{5}\left(i^{2}+\mathrm{i}\right)$ 
B)  $\sum_{i=1}^{5}\left(i^{2}+i-2\right)$ 
C)  $\sum_{i=1}^{5}\left(i^{2}-i\right)$ 
D)  $\sum_{i=1}^{5}(2 i-2)$

Question 8

Expand using the binomial theorem
-$(x+4 y)^{4}$

Accepted Answer

A)  $x^{4}+16 x^{3} y+96 x^{2} y^{2}+256 x y^{3}+256 y^{4}$ 
B)  $x^{4}+16 x^{3} y+128 x^{2} y^{2}+256 x y^{3}+256 y^{4}$ 
C)  $x^{4}+4 x^{3} y+96 x^{2} y^{2}+128 x y^{3}+256 y^{4}$ 
D)  $x^{4}+16 x^{3} y+96 x^{2} y^{2}+16 x y^{3}+256 y^{4}$ 
A)  $x^{4}+16 x^{3} y+96 x^{2} y^{2}+256 x y^{3}+256 y^{4}$ 
B)  $x^{4}+16 x^{3} y+128 x^{2} y^{2}+256 x y^{3}+256 y^{4}$ 
C)  $x^{4}+4 x^{3} y+96 x^{2} y^{2}+128 x y^{3}+256 y^{4}$ 
D)  $x^{4}+16 x^{3} y+96 x^{2} y^{2}+16 x y^{3}+256 y^{4}$

Question 9

Find the partial sum of the geometric sequence with the given first term and common ratio
-$\mathrm{s}_{6}, \mathrm{a}_{1}=2, \mathrm{r}=4$

Accepted Answer

A)  1365 
B)  2730 
C)  42 
D)  84 
A)  1365 
B)  2730 
C)  42 
D)  84

Question 10

Find the indicated partial sum for the sequence with the given general term
-$\mathrm{s}_{5}, \mathrm{a}_{\mathrm{n}}=-4 \mathrm{n}+9$

Accepted Answer

A)  5 
B)  -15 
C)  -11 
D)  25 
A)  5 
B)  -15 
C)  -11 
D)  25

Question 11

Find the common ratio, r, for the geometric sequence
-$8,4,2,1, \ldots$

Accepted Answer

A)  $\frac{1}{2}$ 
B)  1 
C)  $\frac{1}{3}$ 
D)  2 
A)  $\frac{1}{2}$ 
B)  1 
C)  $\frac{1}{3}$ 
D)  2

Question 12

For the given geometric sequence, find the limit of the infinite series, if it exists.
-$24,12,6,3, \ldots$

Accepted Answer

A)  -24 
B)  42 
C)  48 
D)  24 
A)  -24 
B)  42 
C)  48 
D)  24

Question 13

Find the indicated partial sum for the sequence with the given general term
-$s_{4}, a_{n}=-3 n+7$

Accepted Answer

A)  16 
B)  4 
C)  -2 
D)  -5 
A)  16 
B)  4 
C)  -2 
D)  -5

Question 14

Find the indicated term for the sequence.
-Find the $5^{\text {th }}$ term of the sequence whose general term is $a_{n}=3(2 n-2)$.

Accepted Answer

A)  18 
B)  24 
C)  40 
D)  30 
A)  18 
B)  24 
C)  40 
D)  30

Question 15

Find the sum
-$\sum_{i=3}^{6}\left(i^{2}-3\right)$

Accepted Answer

A)  86 
B)  41 
C)  74 
D)  99 
A)  86 
B)  41 
C)  74 
D)  99

Question 16

For the given geometric sequence, find the limit of the infinite series, if it exists.
-$\frac{5}{3} \cdot\left(-\frac{1}{3}\right)^{n-1}$

Accepted Answer

A)  $\frac{5}{3}$ 
B)  No limit 
C)  $\frac{1}{4}$ 
D)  $\frac{5}{4}$ 
A)  $\frac{5}{3}$ 
B)  No limit 
C)  $\frac{1}{4}$ 
D)  $\frac{5}{4}$

Question 17

Find the general term, $a_n$, of the given geometric sequence
-$36,6,1, \ldots$

Accepted Answer

A)  $a_{n}=6(n-1)$ 
B)  $a_{n}=6^{3-n}$ 
C)  $a_{n}=6^{n}$ 
D)  $a_{n}=6^{n-1}$ 
A)  $a_{n}=6(n-1)$ 
B)  $a_{n}=6^{3-n}$ 
C)  $a_{n}=6^{n}$ 
D)  $a_{n}=6^{n-1}$

Question 18

Find the general term, $a_n$, of the given geometric sequence
-$\frac{1}{8}, \frac{1}{64}, \frac{1}{512}, \ldots$

Accepted Answer

A)  $a_{n}=\frac{1}{8^{n-1}+7}$ 
B)  $a_{n}=8^{n-1}$ 
C)  $a_{n}=\frac{1}{8^{n}}$ 
D)  $a_{n}=\frac{1}{8+56(n-1)}$ 
A)  $a_{n}=\frac{1}{8^{n-1}+7}$ 
B)  $a_{n}=8^{n-1}$ 
C)  $a_{n}=\frac{1}{8^{n}}$ 
D)  $a_{n}=\frac{1}{8+56(n-1)}$

Question 19

Find the general term, $a_n$, of the given arithmetic sequence
-$2,4,6,8,10, \ldots$

Accepted Answer

A)  $a_{n}=2 n$ 
B)  $a_{n}=3 n$ 
C)  $a_{n}=n^{2}$ 
D)  $a_{n}=n+2$ 
A)  $a_{n}=2 n$ 
B)  $a_{n}=3 n$ 
C)  $a_{n}=n^{2}$ 
D)  $a_{n}=n+2$

Question 20

Find the indicated partial sum for the given sequence with the given first term and general term
-$\mathrm{s}_{4}, \mathrm{a}_{1}=4, \mathrm{a}_{\mathrm{n}}=\mathrm{a}_{\mathrm{n}}-1+7$

Accepted Answer

A)  90 
B)  58 
C)  33 
D)  54 
A)  90 
B)  58 
C)  33 
D)  54

Use an infinite geometric series to rewrite the repeating decimal as a lowest-terms fraction - $0 . \overline{3825}$

Find the common difference,d, of the given arithmetic sequence - $4,6,8,10, \ldots$

Find the general term $a_n$ of the given sequence - $3,15,27,39,51, \ldots$

Find the partial sum of the geometric sequence with the given first term and common ratio - $\mathrm{s}_{13}, \mathrm{a}_{1}=8, \mathrm{r}=2$

Find the indicated partial sum for the given sequence - $\mathrm{s}_{4},-12,-10,-8,-6, \ldots$

For the given geometric sequence, find the limit of the infinite series, if it exists. - $-10,-5,-\frac{5}{2},-\frac{5}{4}, \ldots$

Write the sum using summation notation - $0+2+6+12+20$

Expand using the binomial theorem - $(x+4 y)^{4}$

Find the partial sum of the geometric sequence with the given first term and common ratio - $\mathrm{s}_{6}, \mathrm{a}_{1}=2, \mathrm{r}=4$

Find the indicated partial sum for the sequence with the given general term - $\mathrm{s}_{5}, \mathrm{a}_{\mathrm{n}}=-4 \mathrm{n}+9$

Find the common ratio, r, for the geometric sequence - $8,4,2,1, \ldots$

For the given geometric sequence, find the limit of the infinite series, if it exists. - $24,12,6,3, \ldots$

Find the indicated partial sum for the sequence with the given general term - $s_{4}, a_{n}=-3 n+7$

Find the indicated term for the sequence. -Find the $5^{\text {th }}$ term of the sequence whose general term is $a_{n}=3(2 n-2)$ .

Find the sum - $\sum_{i=3}^{6}\left(i^{2}-3\right)$

For the given geometric sequence, find the limit of the infinite series, if it exists. - $\frac{5}{3} \cdot\left(-\frac{1}{3}\right)^{n-1}$

Find the general term, $a_n$ , of the given geometric sequence - $36,6,1, \ldots$

Find the general term, $a_n$ , of the given geometric sequence - $\frac{1}{8}, \frac{1}{64}, \frac{1}{512}, \ldots$

Find the general term, $a_n$ , of the given arithmetic sequence - $2,4,6,8,10, \ldots$

Find the indicated partial sum for the given sequence with the given first term and general term - $\mathrm{s}_{4}, \mathrm{a}_{1}=4, \mathrm{a}_{\mathrm{n}}=\mathrm{a}_{\mathrm{n}}-1+7$

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

Use an infinite geometric series to rewrite the repeating decimal as a lowest-terms fraction - 0.3825‾0 . \overline{3825}0.3825

Find the common difference,d, of the given arithmetic sequence - 4,6,8,10,…4,6,8,10, \ldots4,6,8,10,…

Find the general term ana_nan​ of the given sequence - 3,15,27,39,51,…3,15,27,39,51, \ldots3,15,27,39,51,…

Find the partial sum of the geometric sequence with the given first term and common ratio - s13,a1=8,r=2\mathrm{s}_{13}, \mathrm{a}_{1}=8, \mathrm{r}=2s13​,a1​=8,r=2

Find the indicated partial sum for the given sequence - s4,−12,−10,−8,−6,…\mathrm{s}_{4},-12,-10,-8,-6, \ldotss4​,−12,−10,−8,−6,…

For the given geometric sequence, find the limit of the infinite series, if it exists. - −10,−5,−52,−54,…-10,-5,-\frac{5}{2},-\frac{5}{4}, \ldots−10,−5,−25​,−45​,…

Write the sum using summation notation - 0+2+6+12+200+2+6+12+200+2+6+12+20

Expand using the binomial theorem - (x+4y)4(x+4 y)^{4}(x+4y)4

Find the partial sum of the geometric sequence with the given first term and common ratio - s6,a1=2,r=4\mathrm{s}_{6}, \mathrm{a}_{1}=2, \mathrm{r}=4s6​,a1​=2,r=4

Find the indicated partial sum for the sequence with the given general term - s5,an=−4n+9\mathrm{s}_{5}, \mathrm{a}_{\mathrm{n}}=-4 \mathrm{n}+9s5​,an​=−4n+9

Find the common ratio, r, for the geometric sequence - 8,4,2,1,…8,4,2,1, \ldots8,4,2,1,…

For the given geometric sequence, find the limit of the infinite series, if it exists. - 24,12,6,3,…24,12,6,3, \ldots24,12,6,3,…

Find the indicated partial sum for the sequence with the given general term - s4,an=−3n+7s_{4}, a_{n}=-3 n+7s4​,an​=−3n+7

Find the indicated term for the sequence. -Find the 5th 5^{\text {th }}5th term of the sequence whose general term is an=3(2n−2)a_{n}=3(2 n-2)an​=3(2n−2) .

Find the sum - ∑i=36(i2−3)\sum_{i=3}^{6}\left(i^{2}-3\right)∑i=36​(i2−3)

For the given geometric sequence, find the limit of the infinite series, if it exists. - 53⋅(−13)n−1\frac{5}{3} \cdot\left(-\frac{1}{3}\right)^{n-1}35​⋅(−31​)n−1

Find the general term, ana_nan​ , of the given geometric sequence - 36,6,1,…36,6,1, \ldots36,6,1,…

Find the general term, ana_nan​ , of the given geometric sequence - 18,164,1512,…\frac{1}{8}, \frac{1}{64}, \frac{1}{512}, \ldots81​,641​,5121​,…

Find the general term, ana_nan​ , of the given arithmetic sequence - 2,4,6,8,10,…2,4,6,8,10, \ldots2,4,6,8,10,…

Find the indicated partial sum for the given sequence with the given first term and general term - s4,a1=4,an=an−1+7\mathrm{s}_{4}, \mathrm{a}_{1}=4, \mathrm{a}_{\mathrm{n}}=\mathrm{a}_{\mathrm{n}}-1+7s4​,a1​=4,an​=an​−1+7