Resources

Resources

Write variable expressions for arithmetic sequences

Write an expression to describe the sequence below. Use

n

to represent the position of a term in the sequence, where

n = 1

for the first term.

\newline

–31, –30, –29, –28, \ldots

\newline

a_n =

Write an expression to describe the sequence below. Use

n

to represent the position of a term in the sequence, where

n = 1

for the first term.

\newline

31, 32, 33, 34, \ldots

\newline

a_n =

Write an expression to describe the sequence below. Use

n

to represent the position of a term in the sequence, where

n = 1

for the first term.

\newline

73, 146, 219, 292, \ldots

\newline

a_n =

Given the definitions of

f(x)

g(x)

below, find the value of

f(g(2))

\newline

\begin{array}{l} f(x)=-3 x-1 \\ g(x)=3 x^{2}-6 x+8 \end{array}

\newline

Rewrite in simplest terms:

0.1(-3 y-7 z)-z-0.2(-7 z+4 y)

\newline

Rewrite in simplest terms:

7(-7 n+6 p)+0.9 p-8(-8 p-5 n)

\newline

Find an explicit formula for the geometric sequence

\newline

-25,-50,-100,-200,\dots

\newline

Note: the first term should be

d(1)

\newline

d(n)=

Which of the following are real numbers?

\newline

Multi-select Choices:

\newline

10

\newline

\frac{9}{10}

\newline

1.444\ldots

\newline

3

Write an explicit formula for

a_{n}

n^{\text {th }}

term of the sequence

9,14,19, \ldots

\newline

a_{n}=

\newline

Write an explicit formula for

a_{n}

n^{\text {th }}

term of the sequence

27,23,19, \ldots

\newline

a_{n}=

Write an explicit formula for

a_{n}

n^{\text {th }}

term of the sequence

37,31,25, \ldots

\newline

a_{n}=

Write an explicit formula for

a_{n}

n^{\text {th }}

term of the sequence

5,-10,20, \ldots

\newline

a_{n}=

\newline

Write an explicit formula for

a_{n}

n^{\text {th }}

term of the sequence

80,20,5, \ldots

\newline

a_{n}=

\newline

Write an explicit formula that represents the sequence defined by the following recursive formula:

\newline

a_{1}=3 \text { and } a_{n}=2 a_{n-1}

\newline

a_{n}=

Write an explicit formula that represents the sequence defined by the following recursive formula:

\newline

a_{1}=3 \text { and } a_{n}=a_{n-1}+7

\newline

a_{n}=

Write an explicit formula that represents the sequence defined by the following recursive formula:

\newline

a_{1}=9 \text { and } a_{n}=\frac{1}{3} a_{n-1}

\newline

a_{n}=

Write an explicit formula that represents the sequence defined by the following recursive formula:

\newline

a_{1}=125 \text { and } a_{n}=\frac{1}{5} a_{n-1}

\newline

a_{n}=

Write an explicit formula that represents the sequence defined by the following recursive formula:

\newline

a_{1}=8 \text { and } a_{n}=3 a_{n-1}

\newline

a_{n}=

Write an explicit formula that represents the sequence defined by the following recursive formula:

\newline

a_{1}=144 \text { and } a_{n}=\frac{1}{6} a_{n-1}

\newline

a_{n}=

11

th term of the geometric sequence shown below.

\newline

-3 x^{2}, 9 x^{6},-27 x^{10}, \ldots

\newline

Simplify the following expression completely.

\newline

\frac{x^{2}-x-30}{x^{2}-7 x+6}

\newline

For the function

f(x)=\frac{6-x}{8-5 x}

f^{-1}(x)

\newline

f^{-1}(x)=

Evaluate the left hand side to find the value of

a

in the equation in simplest form.

\newline

\frac{x^{\frac{2}{3}}}{x^{\frac{1}{2}}}=x^{a}

\newline

Write an explicit formula for

a_{n}

n^{\text {th }}

term of the sequence

1,-4,16, \ldots

\newline

a_{n}=

Given the function

y=\frac{6+x^{2}}{3 x+2}

\frac{d y}{d x}

in simplified form.

\newline

\frac{d y}{d x}=

Given the function

f(x)=\frac{x^{3}-1}{6+x^{3}}

f^{\prime}(x)

in simplified form.

\newline

f^{\prime}(x)=

Given the substitutions

\ln 2=a, \ln 3=b

\ln 5=c

, find the value of

\ln \left(\frac{4}{\sqrt{3}}\right)

a, b

c

\newline

f(x)=x^{\frac{3}{2}}

\newline

f^{\prime}(x)=

h(x)=\frac{\ln (x)}{x^{2}}

\newline

h^{\prime}(x)=

f

be a function such that

f(2)=-4

f^{\prime}(2)=4

\newline

g

be the function

g(x)=2 x^{2}

\newline

G

be a function defined as

G(x)=\frac{f(x)}{g(x)}

\newline

G^{\prime}(2)=

h(x)=2^{x}

\newline

h^{\prime \prime}(x)

\newline

h^{\prime \prime}(x)=

Write an expression to describe the sequence below. Use

n

to represent the position of a term in the sequence, where

n = 1

for the first term.

\newline

73, 74, 75, 76, \ldots

\newline

a_n =