Question 1

Find the 7th term of $(x-3) 11$.

Accepted Answer

A)  $336,798 \mathrm{x}^{5}$ 
B)  $-721,710 x^{6}$ 
C)  $240,570 x 5$ 
D)  - 112, $266 \mathrm{x}^{6}$ 
A)  $336,798 \mathrm{x}^{5}$ 
B)  $-721,710 x^{6}$ 
C)  $240,570 x 5$ 
D)  - 112, $266 \mathrm{x}^{6}$ A

Question 2

Find the sum of the first ten terms of the geometric progression $2,3,4.5,6.65, \ldots$

Accepted Answer

A)  $\frac{59049}{256}$ 
B)  $\frac{58025}{512}$ 
C)  $\frac{58025}{256}$ 
D)  $\frac{59049}{512}$ 
A)  $\frac{59049}{256}$ 
B)  $\frac{58025}{512}$ 
C)  $\frac{58025}{256}$ 
D)  $\frac{59049}{512}$ C

Question 3

For the problems below, find the nth term of the geometric progression.
- $2, \frac{1}{2}, \frac{1}{8}, \ldots, \mathrm{n}=7$

Accepted Answer

-2-11

Question 4

For the problems below find the sum of the first $\mathrm{n}$ terms.
-  $81,27,9, \ldots, n=6$

Accepted Answer

The answer of For the problems below find the sum...

Question 5

For the problems below, find the nth term of the geometric progression.
- $4,12,36, \ldots, n=5$

Accepted Answer

The answer of For the problems below, find the nth...

Question 6

For the problems below, find the nth term of the geometric progression.
-  $-5,-10,-20, \ldots, n=10$

Accepted Answer

The answer of For the problems below, find the nth...

Question 7

Find the 9th term of the geometric progression $1, \frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \ldots$

Accepted Answer

A)  $\frac{1}{2187}$ 
B)  $\frac{1}{19683}$ 
C)  $\frac{1}{6561}$ 
D)  $\frac{1}{59049}$ 
A)  $\frac{1}{2187}$ 
B)  $\frac{1}{19683}$ 
C)  $\frac{1}{6561}$ 
D)  $\frac{1}{59049}$

Question 8

Find the 56th term in an arithmetic progression where $\mathrm{a}=3$ and $\mathrm{d}=1.5$.

Accepted Answer

A)  85.5 
B)  87 
C)  79.5 
D)  82.5 
A)  85.5 
B)  87 
C)  79.5 
D)  82.5

Question 9

For the problems below, find the sum of the infinite geometric series, if possible.
-  $\frac{1}{2}+1+2+\ldots+\frac{1}{2}(2) \mathrm{n}-1+\ldots$

Accepted Answer

The answer of For the problems below, find the sum...

Question 10

For the problems below find the sum of the first $\mathrm{n}$ terms.
- $a=2, r=3, n=6$

Accepted Answer

The answer of For the problems below find the sum...

Question 11

A sugar syrup is being cooled at the rate of $25 \%$ each minute. Find the temperature of the syrup after 6 minutes if the original temperature was $512^{\circ} \mathrm{F}$. (Hint: The temperature after 1 minute is $384^{\circ} \mathrm{F}$.)

Accepted Answer

The answer of A sugar syrup is being cooled at...

Question 12

For the problems below, find the nth term of the geometric progression.
-  $-9,-3,-1, \ldots, n=8$

Accepted Answer

The answer of For the problems below, find the nth...

Question 13

For the problems below, expand each binomial using the binomial theorem.
-  $(x+4 y)^{4}$

Accepted Answer

The answer of For the problems below, expand each binomial...

Question 14

For the problems below, expand each binomial using the binomial theorem.
-  $(4 \mathrm{x}-3 \mathrm{y})^{5}$

Accepted Answer

The answer of For the problems below, expand each binomial...

Question 15

For the problems below find the sum of the first $\mathrm{n}$ terms.
-Carmen is employed at an initial salary of $\$ 32,000$. If she receives an annual raise of $\$ 1100$, what is her salary for the eighth year?

Accepted Answer

The answer of For the problems below find the sum...

Question 16

For the problems below find the sum of the first $\mathrm{n}$ terms.
- $a=3, \ell=-9, n=7$

Accepted Answer

The answer of For the problems below find the sum...

Question 17

For the problems below, find the indicated term of each binomial expansion.
- $(3 x-5 y)^{6}$ third term

Accepted Answer

The answer of For the problems below, find the indicated...

Question 18

For the problems below find the nth term of the arithmetic progression.
- $2,-1,-4, \ldots, n=8$

Accepted Answer

The answer of For the problems below find the nth...

Question 19

The first term of an arithmetic progression is 15 and the 50th term is - 107.5. Find the common difference, $\mathrm{d}$.

Accepted Answer

A)  -3.5 
B)  -2 
C)  -2.5 
D)  -3 
A)  -3.5 
B)  -2 
C)  -2.5 
D)  -3

Question 20

For the problems below find the nth term of the arithmetic progression.
-  $-1,0.5,2, \ldots, \mathrm{n}=17$

Accepted Answer

The answer of For the problems below find the nth...

Find the 7th term of $(x-3) 11$ .

Find the sum of the first ten terms of the geometric progression $2,3,4.5,6.65, \ldots$

For the problems below, find the nth term of the geometric progression. - $2, \frac{1}{2}, \frac{1}{8}, \ldots, \mathrm{n}=7$

For the problems below find the sum of the first $\mathrm{n}$ terms. - $81,27,9, \ldots, n=6$

For the problems below, find the nth term of the geometric progression. - $4,12,36, \ldots, n=5$

For the problems below, find the nth term of the geometric progression. - $-5,-10,-20, \ldots, n=10$

Find the 9th term of the geometric progression $1, \frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \ldots$

Find the 56th term in an arithmetic progression where $\mathrm{a}=3$ and $\mathrm{d}=1.5$ .

For the problems below, find the sum of the infinite geometric series, if possible. - $\frac{1}{2}+1+2+\ldots+\frac{1}{2}(2) \mathrm{n}-1+\ldots$

For the problems below find the sum of the first $\mathrm{n}$ terms. - $a=2, r=3, n=6$

A sugar syrup is being cooled at the rate of $25 \%$ each minute. Find the temperature of the syrup after 6 minutes if the original temperature was $512^{\circ} \mathrm{F}$ . (Hint: The temperature after 1 minute is $384^{\circ} \mathrm{F}$ .)

For the problems below, find the nth term of the geometric progression. - $-9,-3,-1, \ldots, n=8$

For the problems below, expand each binomial using the binomial theorem. - $(x+4 y)^{4}$

For the problems below, expand each binomial using the binomial theorem. - $(4 \mathrm{x}-3 \mathrm{y})^{5}$

For the problems below find the sum of the first $\mathrm{n}$ terms. -Carmen is employed at an initial salary of $\$ 32,000$ . If she receives an annual raise of $\$ 1100$ , what is her salary for the eighth year?

For the problems below find the sum of the first $\mathrm{n}$ terms. - $a=3, \ell=-9, n=7$

For the problems below, find the indicated term of each binomial expansion. - $(3 x-5 y)^{6}$ third term

For the problems below find the nth term of the arithmetic progression. - $2,-1,-4, \ldots, n=8$

The first term of an arithmetic progression is 15 and the 50th term is - 107.5. Find the common difference, $\mathrm{d}$ .

For the problems below find the nth term of the arithmetic progression. - $-1,0.5,2, \ldots, \mathrm{n}=17$

Analytic Geometry

The Derivative

Applications of the Derivative

Derivatives of Transcendental Functions

The Integral

Applications of Integration

Methods of Integration

Three-Space: Partial Derivatives and Double Integrals

Series

First-Order Differential Equations

Second-Order Differential Equations

Filters

Exam 9: Progressions and the Binomial Theorem

Find the 7th term of (x−3)11(x-3) 11(x−3)11 .

Find the sum of the first ten terms of the geometric progression 2,3,4.5,6.65,…2,3,4.5,6.65, \ldots2,3,4.5,6.65,…

For the problems below, find the nth term of the geometric progression. - 2,12,18,…,n=72, \frac{1}{2}, \frac{1}{8}, \ldots, \mathrm{n}=72,21​,81​,…,n=7

For the problems below find the sum of the first n\mathrm{n}n terms. - 81,27,9,…,n=681,27,9, \ldots, n=681,27,9,…,n=6

For the problems below, find the nth term of the geometric progression. - 4,12,36,…,n=54,12,36, \ldots, n=54,12,36,…,n=5

For the problems below, find the nth term of the geometric progression. - −5,−10,−20,…,n=10-5,-10,-20, \ldots, n=10−5,−10,−20,…,n=10

Find the 9th term of the geometric progression 1,13,19,127,…1, \frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \ldots1,31​,91​,271​,…

Find the 56th term in an arithmetic progression where a=3\mathrm{a}=3a=3 and d=1.5\mathrm{d}=1.5d=1.5 .

For the problems below, find the sum of the infinite geometric series, if possible. - 12+1+2+…+12(2)n−1+…\frac{1}{2}+1+2+\ldots+\frac{1}{2}(2) \mathrm{n}-1+\ldots21​+1+2+…+21​(2)n−1+…

For the problems below find the sum of the first n\mathrm{n}n terms. - a=2,r=3,n=6a=2, r=3, n=6a=2,r=3,n=6

A sugar syrup is being cooled at the rate of 25%25 \%25% each minute. Find the temperature of the syrup after 6 minutes if the original temperature was 512∘F512^{\circ} \mathrm{F}512∘F . (Hint: The temperature after 1 minute is 384∘F384^{\circ} \mathrm{F}384∘F .)

For the problems below, find the nth term of the geometric progression. - −9,−3,−1,…,n=8-9,-3,-1, \ldots, n=8−9,−3,−1,…,n=8

For the problems below, expand each binomial using the binomial theorem. - (x+4y)4(x+4 y)^{4}(x+4y)4

For the problems below, expand each binomial using the binomial theorem. - (4x−3y)5(4 \mathrm{x}-3 \mathrm{y})^{5}(4x−3y)5

For the problems below find the sum of the first n\mathrm{n}n terms. -Carmen is employed at an initial salary of $32,000\$ 32,000$32,000 . If she receives an annual raise of $1100\$ 1100$1100 , what is her salary for the eighth year?

For the problems below find the sum of the first n\mathrm{n}n terms. - a=3,ℓ=−9,n=7a=3, \ell=-9, n=7a=3,ℓ=−9,n=7

For the problems below, find the indicated term of each binomial expansion. - (3x−5y)6(3 x-5 y)^{6}(3x−5y)6 third term

For the problems below find the nth term of the arithmetic progression. - 2,−1,−4,…,n=82,-1,-4, \ldots, n=82,−1,−4,…,n=8

The first term of an arithmetic progression is 15 and the 50th term is - 107.5. Find the common difference, d\mathrm{d}d .

For the problems below find the nth term of the arithmetic progression. - −1,0.5,2,…,n=17-1,0.5,2, \ldots, \mathrm{n}=17−1,0.5,2,…,n=17

Analytic Geometry

The Derivative

Applications of the Derivative

Derivatives of Transcendental Functions

The Integral

Applications of Integration

Methods of Integration

Three-Space: Partial Derivatives and Double Integrals

Series

First-Order Differential Equations

Second-Order Differential Equations

Filters

Find the 7th term of $(x-3) 11$ .

Find the sum of the first ten terms of the geometric progression $2,3,4.5,6.65, \ldots$

For the problems below, find the nth term of the geometric progression. - $2, \frac{1}{2}, \frac{1}{8}, \ldots, \mathrm{n}=7$

For the problems below find the sum of the first $\mathrm{n}$ terms. - $81,27,9, \ldots, n=6$

For the problems below, find the nth term of the geometric progression. - $4,12,36, \ldots, n=5$

For the problems below, find the nth term of the geometric progression. - $-5,-10,-20, \ldots, n=10$

Find the 9th term of the geometric progression $1, \frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \ldots$

Find the 56th term in an arithmetic progression where $\mathrm{a}=3$ and $\mathrm{d}=1.5$ .

For the problems below, find the sum of the infinite geometric series, if possible. - $\frac{1}{2}+1+2+\ldots+\frac{1}{2}(2) \mathrm{n}-1+\ldots$

For the problems below find the sum of the first $\mathrm{n}$ terms. - $a=2, r=3, n=6$

A sugar syrup is being cooled at the rate of $25 \%$ each minute. Find the temperature of the syrup after 6 minutes if the original temperature was $512^{\circ} \mathrm{F}$ . (Hint: The temperature after 1 minute is $384^{\circ} \mathrm{F}$ .)

For the problems below, find the nth term of the geometric progression. - $-9,-3,-1, \ldots, n=8$

For the problems below, expand each binomial using the binomial theorem. - $(x+4 y)^{4}$

For the problems below, expand each binomial using the binomial theorem. - $(4 \mathrm{x}-3 \mathrm{y})^{5}$

For the problems below find the sum of the first $\mathrm{n}$ terms. -Carmen is employed at an initial salary of $\$ 32,000$ . If she receives an annual raise of $\$ 1100$ , what is her salary for the eighth year?

For the problems below find the sum of the first $\mathrm{n}$ terms. - $a=3, \ell=-9, n=7$

For the problems below, find the indicated term of each binomial expansion. - $(3 x-5 y)^{6}$ third term

For the problems below find the nth term of the arithmetic progression. - $2,-1,-4, \ldots, n=8$

The first term of an arithmetic progression is 15 and the 50th term is - 107.5. Find the common difference, $\mathrm{d}$ .

For the problems below find the nth term of the arithmetic progression. - $-1,0.5,2, \ldots, \mathrm{n}=17$