Question 1

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: 8 feet; rebounds $70 \%$

Accepted Answer

A)  18.7 feet 
B)  45.3 feet 
C)  26.7 feet 
D)  30.1 feet

Question 2

Find the common ratio, r, for the geometric sequence
-$1,-3,9,-27,81, \ldots$

Accepted Answer

A)  -4 
B)  81 
C)  3 
D)  -3

Question 3

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 70 cubed positive integers.

Accepted Answer

A)  $24,700,900$ 
B)  116,795 
C)  $12,350,450$ 
D)  $6,175,225$

Question 4

Find the first five terms of the arithmetic sequence with the given first term and common difference
-$\mathrm{a}_{1}=-17, \mathrm{~d}=4$

Accepted Answer

A)  $-1,-5,-9,-13,-17$ 
B)  - $17,-13,-9,-5,-1$ 
C)  $-9,-5,-1,3,7$ 
D)  $-9,-13,-17,-21,-25$

Question 5

Find the indicated partial sum for the given sequence
-$s_{6}, 5,7,9,11, \ldots$

Accepted Answer

A)  5 
B)  30 
C)  60 
D)  17

Question 6

Write the sum using summation notation
-$18+30+42+54+66$

Accepted Answer

A)  $\sum_{i=1}^{5}(12 i+6)$ 
B)  $\sum_{i=1}^{5}(12 n+6)$ 
C)  $\sum_{i=1}^{6}(12 i+6)$ 
D)  $\sum_{i=0}^{5}(12 i+6)$

Question 7

Find the first five terms of the sequence with the given general term.
-$a_{n}=(-1)^{n+1}$

Accepted Answer

A)  $-1,-1,-1,-1,-1$ 
B)  1, 1, 1, 1, 1 
C)  $-1,1,-1,1,-1$ 
D)  1, - 1, 1, - 1, 1

Question 8

Find the indicated partial sum for the given sequence
-$s_{6}, 3,-8,13,-18, \ldots$

Accepted Answer

A)  -12 
B)  - 15 
C)  15 
D)  8

Question 9

For the given geometric sequence, find the limit of the infinite series, if it exists.
-$a_{n}=4 \cdot(1)^{n}$

Accepted Answer

A)  3072 
B)  No limit 
C)  1886 
D)  3441

Question 10

Solve the problem.
-Jackie is considering a job that offers a monthly starting salary of $\$ 2500$ and guarantees her a monthly raise of $\$ 140$ during her first year on the job. Find the general term of this arithmetic sequence and her monthly salary at the end of her first year.

Accepted Answer

A)  $a_{n}=2500+140 \mathrm{n} ; \$ 4040$ 
B)  $a_{n}=2500+140 \mathrm{n} ; \$ 4180$ 
C)  $a_{n}=2360+140 \mathrm{n} ; \$ 4040$ 
D)  $a_{n}=2360+140(n-1) ; \$ 3900$

Question 11

Find the indicated term.
-Which term of the arithmetic sequence $11,6,1, \ldots$, is equal to - 489 ?

Accepted Answer

A)  Term 96 
B)  Term 101 
C)  Term 91 
D)  Term 116

Question 12

Find the general term $a_n$ of the given sequence
-$2,6,10,14,18, \ldots$

Accepted Answer

A)  $a_{n}=2 n-4$ 
B)  $\mathrm{a}_{\mathrm{n}}=\mathrm{n}+4$ 
C)  $a_{n}=4 n-2$ 
D)  $a_{n}=2(4)^{n-1}$

Question 13

Simplify.
-$\frac{7 !}{0 ! \cdot 7 !}$

Accepted Answer

A)  5040 
B)  7 
C)  0 
D)  1

Question 14

Find the indicated partial sum for the given sequence
-s8, $1,-5,9,-13, \ldots$

Accepted Answer

A)  -15 
B)  16 
C)  5 
D)  -16

Question 15

Find the indicated term for the sequence.
-Find the $11^{\text {th }}$ term of the sequence whose general term is $a_{n}=n^{2}-n$.

Accepted Answer

A)  11 
B)  132 
C)  110 
D)  -110

Question 16

Solve the problem.
-The number of students in a school in year $n$ is estimated by the model $a_{n}=6 n^{2}+13 n+83$. Write a sequence showing how many students are in the school in each of the first three years.

Accepted Answer

A)  $102,133,176$ 
B)  $108,133,176$ 
C)  $115,146,189$ 
D)  $102,133,158$

Question 17

Solve.
-One approximation for Euler's number e is the infinite sum $1+\sum_{\mathrm{i}=1}^{\infty} \frac{1}{\mathrm{i} !}=1+$ $\left.\left(\frac{1}{1}+\frac{1}{1 \cdot 2}+\frac{1}{1 \cdot 2 \cdot 3}+\frac{1}{1 \cdot 2 \cdot 3 \cdot 4}+\ldots\right).\right)$ The expression $\mathrm{i}$ ! is called $\mathrm{i}$ factorial and is equal to the product of the integers from 1 through $i$. Find the sum through $i=9$, rounded to the nearest thousandth.

Accepted Answer

A)  2.717 
B)  2.718 
C)  2.708 
D)  2.709

Question 18

Simplify.
-8 !

Accepted Answer

A)  $1,307,674,368,000$ 
B)  40,320 
C)  5040 
D)  362,880

Question 19

Find the sum
-$\sum_{i=1}^{4}\left(i^{2}-5 i-3\right)$

Accepted Answer

A)  0 
B)  -32 
C)  -24 
D)  13

Question 20

Find the general term, $a_n$, of the given geometric sequence
-$\frac{1}{6}, \frac{1}{2}, \frac{3}{2}, \ldots$

Accepted Answer

A)  $a_{n}=\frac{1}{6}+\frac{1}{3}(n-1)$ 
B)  $\mathrm{a}_{\mathrm{n}}=\frac{1}{6}+3(\mathrm{n}-1)$ 
C)  $a_{n}=\frac{1}{6}(3)^{n-1}$ 
D)  $a_{n}=\left(\frac{1}{6}\right)^{n-1}+\frac{1}{3}$

Exam 11: Sequences, Series, and the Binomial Theorem

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: 8 feet; rebounds $70 \%$

Find the common ratio, r, for the geometric sequence - $1,-3,9,-27,81, \ldots$

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 70 cubed positive integers.

Find the first five terms of the arithmetic sequence with the given first term and common difference - $\mathrm{a}_{1}=-17, \mathrm{~d}=4$

Find the indicated partial sum for the given sequence - $s_{6}, 5,7,9,11, \ldots$

Write the sum using summation notation - $18+30+42+54+66$

Find the first five terms of the sequence with the given general term. - $a_{n}=(-1) ^{n+1}$

Find the indicated partial sum for the given sequence - $s_{6}, 3,-8,13,-18, \ldots$

For the given geometric sequence, find the limit of the infinite series, if it exists. - $a_{n}=4 \cdot(1) ^{n}$

Solve the problem. -Jackie is considering a job that offers a monthly starting salary of $\$ 2500$ and guarantees her a monthly raise of $\$ 140$ during her first year on the job. Find the general term of this arithmetic sequence and her monthly salary at the end of her first year.

Find the indicated term. -Which term of the arithmetic sequence $11,6,1, \ldots$ , is equal to - 489 ?

Find the general term $a_n$ of the given sequence - $2,6,10,14,18, \ldots$

Simplify. - $\frac{7 !}{0 ! \cdot 7 !}$

Find the indicated partial sum for the given sequence -s8, $1,-5,9,-13, \ldots$

Find the indicated term for the sequence. -Find the $11^{\text {th }}$ term of the sequence whose general term is $a_{n}=n^{2}-n$ .

Solve the problem. -The number of students in a school in year $n$ is estimated by the model $a_{n}=6 n^{2}+13 n+83$ . Write a sequence showing how many students are in the school in each of the first three years.

Simplify. -8 !

Find the sum - $\sum_{i=1}^{4}\left(i^{2}-5 i-3\right)$

Find the general term, $a_n$ , of the given geometric sequence - $\frac{1}{6}, \frac{1}{2}, \frac{3}{2}, \ldots$

Exam 11: Sequences, Series, and the Binomial Theorem

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: 8 feet; rebounds 70%70 \%70%

Find the common ratio, r, for the geometric sequence - 1,−3,9,−27,81,…1,-3,9,-27,81, \ldots1,−3,9,−27,81,…

Find the first five terms of the arithmetic sequence with the given first term and common difference - a1=−17, d=4\mathrm{a}_{1}=-17, \mathrm{~d}=4a1​=−17, d=4

Find the indicated partial sum for the given sequence - s6,5,7,9,11,…s_{6}, 5,7,9,11, \ldotss6​,5,7,9,11,…

Write the sum using summation notation - 18+30+42+54+6618+30+42+54+6618+30+42+54+66

Find the first five terms of the sequence with the given general term. - an=(−1) n+1a_{n}=(-1) ^{n+1}an​=(−1) n+1

Find the indicated partial sum for the given sequence - s6,3,−8,13,−18,…s_{6}, 3,-8,13,-18, \ldotss6​,3,−8,13,−18,…

For the given geometric sequence, find the limit of the infinite series, if it exists. - an=4⋅(1) na_{n}=4 \cdot(1) ^{n}an​=4⋅(1) n

Solve the problem. -Jackie is considering a job that offers a monthly starting salary of $2500\$ 2500$2500 and guarantees her a monthly raise of $140\$ 140$140 during her first year on the job. Find the general term of this arithmetic sequence and her monthly salary at the end of her first year.

Find the indicated term. -Which term of the arithmetic sequence 11,6,1,…11,6,1, \ldots11,6,1,… , is equal to - 489 ?

Find the general term ana_nan​ of the given sequence - 2,6,10,14,18,…2,6,10,14,18, \ldots2,6,10,14,18,…

Simplify. - 7!0!⋅7!\frac{7 !}{0 ! \cdot 7 !}0!⋅7!7!​

Find the indicated partial sum for the given sequence -s8, 1,−5,9,−13,…1,-5,9,-13, \ldots1,−5,9,−13,…

Find the indicated term for the sequence. -Find the 11th 11^{\text {th }}11th term of the sequence whose general term is an=n2−na_{n}=n^{2}-nan​=n2−n .

Solve the problem. -The number of students in a school in year nnn is estimated by the model an=6n2+13n+83a_{n}=6 n^{2}+13 n+83an​=6n2+13n+83 . Write a sequence showing how many students are in the school in each of the first three years.