Question 1

Find the common ratio, r, for the geometric sequence
-$\frac{3}{4}, \frac{3}{8}, \frac{3}{16}, \frac{3}{32}, \frac{3}{64}, \ldots$

Accepted Answer

A)  2 
B)  $\frac{1}{2}$ 
C)  $\frac{1}{12}$ 
D)  12 
A)  2 
B)  $\frac{1}{2}$ 
C)  $\frac{1}{12}$ 
D)  12

Question 2

Simplify.
-$\frac{5 !}{3 ! \cdot 2 !}$

Accepted Answer

A)  20 
B)  10 
C)  120 
D)  60 
A)  20 
B)  10 
C)  120 
D)  60

Question 3

Find the sum
-$\sum_{i=1}^{6}(6 i-3)$

Accepted Answer

A)  76 
B)  75 
C)  108 
D)  1165 
A)  76 
B)  75 
C)  108 
D)  1165

Question 4

Expand using the binomial theorem
-$(x-5)^{4}$

Accepted Answer

A)  $x^{4}-20 x^{3}-250 x^{2}-500 x+625$ 
B)  $x^{4}-5 x^{3}+150 x^{2}-250 x+625$ 
C)  $x^{4}-20 x^{3}+150 x^{2}+20 x+625$ 
D)  $x^{4}-20 x^{3}+150 x^{2}-500 x+625$ 
A)  $x^{4}-20 x^{3}-250 x^{2}-500 x+625$ 
B)  $x^{4}-5 x^{3}+150 x^{2}-250 x+625$ 
C)  $x^{4}-20 x^{3}+150 x^{2}+20 x+625$ 
D)  $x^{4}-20 x^{3}+150 x^{2}-500 x+625$

Question 5

Find the indicated term.
-Find the 17th term of the arithmetic sequence 5, 8, 11, ....

Accepted Answer

A)  -43 
B)  48 
C)  56 
D)  53 
A)  -43 
B)  48 
C)  56 
D)  53

Question 6

Find the indicated partial sum for the sequence with the given general term
-$\mathrm{s}_{3}, \mathrm{a}_{\mathrm{n}}=(\mathrm{n}+2)(\mathrm{n}-6)$

Accepted Answer

A)  46 
B)  -46 
C)  98 
D)  -31 
A)  46 
B)  -46 
C)  98 
D)  -31

Question 7

Find the indicated partial sum for the sequence with the given general term
-$\mathrm{s} 4, \mathrm{a}_{\mathrm{n}}=2 \mathrm{n}-9$

Accepted Answer

A)  -16 
B)  -1 
C)  -7 
D)  -28 
A)  -16 
B)  -1 
C)  -7 
D)  -28

Question 8

Find the first five terms of the arithmetic sequence with the given first term and common difference
-$\mathrm{a}_{1}=6, \mathrm{~d}=-1$

Accepted Answer

A)  $5,4,3,2,1$ 
B)  $6,5,4,3,2$ 
C)  $6,5,3,3,2$ 
D)  $7,6,5,4,3$ 
A)  $5,4,3,2,1$ 
B)  $6,5,4,3,2$ 
C)  $6,5,3,3,2$ 
D)  $7,6,5,4,3$

Question 9

The Fibonacci sequence is a sequence whose first two terms are $f_{1}=1$ and $f_{2}=1$, and all other terms are the sum of the two preceding terms. The terms of the Fibonacci sequence are often referred to as Fibonacci numbers.
-One interesting fact about the Fibonacci numbers is that for any $n \geq 3$,
$2 \cdot f_{n}-f_{n+1}=f_{n}-2$. Select a Fibonacci number, and verify this fact.

Accepted Answer

Answers will vary. F

Question 10

For the given geometric sequence, find the limit of the infinite series, if it exists.
-$3,1, \frac{1}{3}, \frac{1}{9}, \ldots$

Accepted Answer

A)  $\frac{9}{2}$ 
B)  4 
C)  3 
D)  1 
A)  $\frac{9}{2}$ 
B)  4 
C)  3 
D)  1

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} 
-\(\sum_{i=5}^{31} i^{2}$

Accepted Answer

A)  245,791 
B)  10,386 
C)  75,900 
D)  116,795 
A)  245,791 
B)  10,386 
C)  75,900 
D)  116,795

Question 12

For the given geometric sequence, find the limit of the infinite series, if it exists.
-$3,-\frac{3}{4}, \frac{3}{16},-\frac{3}{64}, \ldots$

Accepted Answer

A)  $\frac{12}{5}$ 
B)  $-\frac{3}{4}$ 
C)  3 
D)  $\frac{9}{4}$ 
A)  $\frac{12}{5}$ 
B)  $-\frac{3}{4}$ 
C)  3 
D)  $\frac{9}{4}$

Question 13

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_{\mathrm{i}=1}^{15}\left(\mathrm{i}^{2}+\mathrm{i}\right)$

Accepted Answer

A)  14,520 
B)  18,120 
C)  5440 
D)  1360 
A)  14,520 
B)  18,120 
C)  5440 
D)  1360

Question 14

Write the sum using summation notation
-$\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}$

Accepted Answer

A)  $\sum_{i=0}^{4} \frac{1}{i+5}$ 
B)  $\sum_{\mathrm{i}=1}^{5} \frac{1}{\mathrm{i}+6}$ 
C)  $\sum_{i=0}^{4} \frac{1}{i+6}$ 
D)  $\sum_{i=1}^{5} \frac{1}{i+5}$ 
A)  $\sum_{i=0}^{4} \frac{1}{i+5}$ 
B)  $\sum_{\mathrm{i}=1}^{5} \frac{1}{\mathrm{i}+6}$ 
C)  $\sum_{i=0}^{4} \frac{1}{i+6}$ 
D)  $\sum_{i=1}^{5} \frac{1}{i+5}$

Question 15

Expand using the binomial theorem
-$(x+4)^{3}$

Accepted Answer

A)  $x^{3}+12 x^{2}+48 x+64$ 
B)  $x^{3}+4 x^{2}+8 x+64$ 
C)  $x^{3}+12 x^{2}+12 x+64$ 
D)  $x^{3}+12 x^{2}+8 x+64$ 
A)  $x^{3}+12 x^{2}+48 x+64$ 
B)  $x^{3}+4 x^{2}+8 x+64$ 
C)  $x^{3}+12 x^{2}+12 x+64$ 
D)  $x^{3}+12 x^{2}+8 x+64$

Question 16

Expand using the binomial theorem
-$(x-1)^{6}$

Accepted Answer

A)  $x^{6}-6 x^{5}+15 x^{4}-20 x^{3}+15 x^{2}-6 x+1$ 
B)  $x^{6}-6 x^{5}-15 x^{4}-20 x^{3}-15 x^{2}-6 x-6$ 
C)  $x^{6}-6 x^{5}-30 x^{4}-120 x^{3}-360 x^{2}-720 x+720$ 
D)  $x^{6}-6 x^{5}+30 x^{4}-120 x^{3}+30 x^{2}-6 x+1$ 
A)  $x^{6}-6 x^{5}+15 x^{4}-20 x^{3}+15 x^{2}-6 x+1$ 
B)  $x^{6}-6 x^{5}-15 x^{4}-20 x^{3}-15 x^{2}-6 x-6$ 
C)  $x^{6}-6 x^{5}-30 x^{4}-120 x^{3}-360 x^{2}-720 x+720$ 
D)  $x^{6}-6 x^{5}+30 x^{4}-120 x^{3}+30 x^{2}-6 x+1$

Question 17

Find the indicated partial sum for the given sequence
-$\mathrm{s} _{10},-17,54,125, \ldots$

Accepted Answer

A)  -3110 
B)  -3365 
C)  3110 
D)  3025 
A)  -3110 
B)  -3365 
C)  3110 
D)  3025

Question 18

Find the general term, $a_n$, of the given arithmetic sequence
-$3,12,21,30,39, \ldots$

Accepted Answer

A)  $a_{n}=3(3 n-2)$ 
B)  $a_{n}=6 n-9$ 
C)  $a_{n}=3(9)^{n-1}$ 
D)  $a_{n}=9 n-2$ 
A)  $a_{n}=3(3 n-2)$ 
B)  $a_{n}=6 n-9$ 
C)  $a_{n}=3(9)^{n-1}$ 
D)  $a_{n}=9 n-2$

Question 19

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

Accepted Answer

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

Question 20

Use an infinite geometric series to rewrite the repeating decimal as a lowest-terms fraction
-$0 . \overline{57}$

Accepted Answer

A)  $\frac{19}{33}$ 
B)  $\frac{6}{11}$ 
C)  $\frac{34}{99}$ 
D)  $\frac{57}{100}$ 
A)  $\frac{19}{33}$ 
B)  $\frac{6}{11}$ 
C)  $\frac{34}{99}$ 
D)  $\frac{57}{100}$

Find the common ratio, r, for the geometric sequence - $\frac{3}{4}, \frac{3}{8}, \frac{3}{16}, \frac{3}{32}, \frac{3}{64}, \ldots$

Simplify. - $\frac{5 !}{3 ! \cdot 2 !}$

Find the sum - $\sum_{i=1}^{6}(6 i-3)$

Expand using the binomial theorem - $(x-5)^{4}$

Find the indicated term. -Find the 17th term of the arithmetic sequence 5, 8, 11, ....

Find the indicated partial sum for the sequence with the given general term - $\mathrm{s}_{3}, \mathrm{a}_{\mathrm{n}}=(\mathrm{n}+2)(\mathrm{n}-6)$

Find the indicated partial sum for the sequence with the given general term - $\mathrm{s} 4, \mathrm{a}_{\mathrm{n}}=2 \mathrm{n}-9$

Find the first five terms of the arithmetic sequence with the given first term and common difference - $\mathrm{a}_{1}=6, \mathrm{~d}=-1$

For the given geometric sequence, find the limit of the infinite series, if it exists. - $3,1, \frac{1}{3}, \frac{1}{9}, \ldots$

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 $\sum_{i=1}^{n} -\sum_{i=5}^{31} i^{2}$

For the given geometric sequence, find the limit of the infinite series, if it exists. - $3,-\frac{3}{4}, \frac{3}{16},-\frac{3}{64}, \ldots$

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 $\sum_{i=1}^{n} -\sum_{\mathrm{i}=1}^{15}\left(\mathrm{i}^{2}+\mathrm{i}\right)$

Write the sum using summation notation - $\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}$

Expand using the binomial theorem - $(x+4)^{3}$

Expand using the binomial theorem - $(x-1)^{6}$

Find the indicated partial sum for the given sequence - $\mathrm{s} _{10},-17,54,125, \ldots$

Find the general term, $a_n$ , of the given arithmetic sequence - $3,12,21,30,39, \ldots$

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

Use an infinite geometric series to rewrite the repeating decimal as a lowest-terms fraction - $0 . \overline{57}$

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

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Filters

Exam 11: Sequences, Series, and the Binomial Theorem

Find the common ratio, r, for the geometric sequence - 34,38,316,332,364,…\frac{3}{4}, \frac{3}{8}, \frac{3}{16}, \frac{3}{32}, \frac{3}{64}, \ldots43​,83​,163​,323​,643​,…

Simplify. - 5!3!⋅2!\frac{5 !}{3 ! \cdot 2 !}3!⋅2!5!​

Find the sum - ∑i=16(6i−3)\sum_{i=1}^{6}(6 i-3)∑i=16​(6i−3)

Expand using the binomial theorem - (x−5)4(x-5)^{4}(x−5)4

Find the indicated term. -Find the 17th term of the arithmetic sequence 5, 8, 11, ....

Find the indicated partial sum for the sequence with the given general term - s3,an=(n+2)(n−6)\mathrm{s}_{3}, \mathrm{a}_{\mathrm{n}}=(\mathrm{n}+2)(\mathrm{n}-6)s3​,an​=(n+2)(n−6)

Find the indicated partial sum for the sequence with the given general term - s4,an=2n−9\mathrm{s} 4, \mathrm{a}_{\mathrm{n}}=2 \mathrm{n}-9s4,an​=2n−9

Find the first five terms of the arithmetic sequence with the given first term and common difference - a1=6, d=−1\mathrm{a}_{1}=6, \mathrm{~d}=-1a1​=6, d=−1

For the given geometric sequence, find the limit of the infinite series, if it exists. - 3,1,13,19,…3,1, \frac{1}{3}, \frac{1}{9}, \ldots3,1,31​,91​,…

Use the formulas ∑i=1ni=n(n+1)2,∑i=1ni2=n(n+1)(2n+1)6\sum_{i=1}^{n} i=\frac{n(n+1)}{2}, \sum_{i=1}^{n} i^{2}=\frac{n(n+1)(2 n+1)}{6}∑i=1n​i=2n(n+1)​,∑i=1n​i2=6n(n+1)(2n+1)​ , and ∑i=1n−∑i=531i2\sum_{i=1}^{n} -\sum_{i=5}^{31} i^{2}∑i=1n​−∑i=531​i2

For the given geometric sequence, find the limit of the infinite series, if it exists. - 3,−34,316,−364,…3,-\frac{3}{4}, \frac{3}{16},-\frac{3}{64}, \ldots3,−43​,163​,−643​,…

Write the sum using summation notation - 17+18+19+110+111\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}71​+81​+91​+101​+111​

Expand using the binomial theorem - (x+4)3(x+4)^{3}(x+4)3

Expand using the binomial theorem - (x−1)6(x-1)^{6}(x−1)6

Find the indicated partial sum for the given sequence - s10,−17,54,125,…\mathrm{s} _{10},-17,54,125, \ldotss10​,−17,54,125,…

Find the general term, ana_nan​ , of the given arithmetic sequence - 3,12,21,30,39,…3,12,21,30,39, \ldots3,12,21,30,39,…

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

Use an infinite geometric series to rewrite the repeating decimal as a lowest-terms fraction - 0.57‾0 . \overline{57}0.57