Resources

Resources

Evaluate recursive formulas for sequences

Find values for

p

q

so that the equation has infinitely many solutions.

2x + p = qx - 16

\newline

p =

\newline

q =

Find values for

p

q

so that the equation has infinitely many solutions.

-7x + p = qx + 1

\newline

p =

\newline

q =

Solve the following equation for

x

. Express your answer in the simplest form.

\newline

-2(3 x+8)=-28 x-35

\newline

Solve the following equation for

x

. Express your answer in the simplest form.

\newline

5(4 x+6)=20 x+30

\newline

x+y=15

\newline

x+y=25

A

10+A=50

t

. You must write your answer in fully simplified form.

\newline

16=14 t

\newline

t=

Solve for a. You must write your answer in fully simplified form.

\newline

12 a=18

\newline

a=

t

. You must write your answer in fully simplified form.

\newline

-10=-10 t

\newline

t=

Solve for b. You must write your answer in fully simplified form.

\newline

9=-2 b

\newline

b=

Which equation has the solution

x=3

\newline

8 x-4=-20

\newline

6 x+7=64

\newline

4 x-7=5

\newline

8 x-1=87

5

years younger than her sister Talat. Myra wants to write an equation for her own age

(m)

given Talat's age

(t)

\newline

How should Myra write her equation?

\newline

1

\newline

t=m+5

\newline

t-m=5

\newline

m=t-5

x

\newline

Enter the solutions from least to greatest.

\newline

5 x^{2}+3=83

\newline

x=

\newline

x=

x

\newline

Enter the solutions from least to greatest.

\newline

-4 x^{2}-7=-11

\newline

x=

\newline

x=

Find the zeros of the function.

\newline

Enter the solutions from least to greatest.

\newline

f(x)=-3 x^{2}+75

\newline

x=

\newline

x=

x

\newline

Enter the solutions from least to greatest.

\newline

-2 x^{2}-9=-107

\newline

x=

\newline

x=

x

\newline

Enter the solutions from least to greatest.

\newline

2 x^{2}-5=13

\newline

x=

\newline

x=

Find the zeros of the function.

\newline

Enter the solutions from least to greatest.

\newline

g(x)=4 x^{2}-484

\newline

x=

\newline

x=

x

\newline

Enter the solutions from least to greatest.

\newline

-x^{2}-8=-33

\newline

x=

\newline

x=

Find the zeros of the function.

\newline

Enter the solutions from least to greatest.

\newline

f(x)=8 x^{2}-800

\newline

x=

\newline

x=

x

\newline

Enter the solutions from least to greatest.

\newline

6 x^{2}+1=487

\newline

x=

\newline

x=

x

\newline

Enter the solutions from least to greatest.

\newline

3 x^{2}+4=436

\newline

x=

\newline

x=

\begin{array}{l}\left\{\begin{array}{l}f(1)=-16 \\ f(n)=-29-f(n-1)\end{array}\right. \\ f(2)=\square\end{array}

\begin{array}{l}\left\{\begin{array}{l}h(1)=-12 \\ h(n)=h(n-1) \cdot n\end{array}\right. \\ h(2)=\end{array}

\begin{array}{l}\left\{\begin{array}{l}h(1)=-2 \\ h(2)=1 \\ h(n)=h(n-2)+h(n-1)\end{array}\right. \\ h(3)=\end{array}

\begin{array}{l}\left\{\begin{array}{l}f(1)=15 \\ f(n)=f(n-1) \cdot n\end{array}\right. \\ f(2)=\square\end{array}

\left\{\begin{array}{l}f(1)=25 \\ f(n)=f(n-1) \cdot\left(-\frac{1}{5}\right)\end{array}\right.

\newline

f(3)=

\begin{array}{l}\left\{\begin{array}{l}h(1)=-10 \\ h(2)=-2 \\ h(n)=h(n-2) \cdot h(n-1)\end{array}\right. \\ h(3)=\end{array}

\begin{array}{l}\left\{\begin{array}{l}h(1)=9 \\ h(n)=h(n-1) \cdot \frac{1}{9}\end{array}\right. \\ h(3)=\square\end{array}

\begin{array}{l}\left\{\begin{array}{l}f(1)=-7 \\ f(n)=f(n-1)+3.5\end{array}\right. \\ f(3)=\square\end{array}

\begin{array}{l}\left\{\begin{array}{l}g(1)=5 \\ g(n)=-1 \cdot g(n-1)-4\end{array}\right. \\ g(2)=\square\end{array}

Abraham is writing a recursive function for the geometric sequence:

\newline

24,12,6,3, \ldots

\newline

He comes up with:

\newline

\left\{\begin{array}{l} s(1)=24 \\ s(n)=s(n-1) \cdot \frac{1}{2} \end{array}\right.

\newline

What domain should Abraham use for

s

so it generates the sequence?

\newline

1

\newline

n \geq 0

n

\newline

n \geq 0

n

\newline

n \geq 1

n

\newline

n \geq 1

n

Raymundo is writing an explicit function for the arithmetic sequence:

\newline

20,15,10,5, \ldots

\newline

He comes up with

\newline

s(n)=20-5 n \text {. }

\newline

What domain should Raymundo use for

s

so it generates the sequence?

\newline

1

\newline

n \geq 0

n

\newline

n \geq 0

n

\newline

n \geq 1

n

\newline

n \geq 1

n

Supriya is writing a recursive function for the arithmetic sequence:

\newline

-11,-6,-1,4, \ldots

\newline

She comes up with:

\newline

\left\{\begin{array}{l} t(0)=-11 \\ t(n)=t(n-1)+5 \end{array}\right.

\newline

What domain should Supriya use for

t

so it generates the sequence?

\newline

1

\newline

n \geq 0

n

\newline

n \geq 0

n

\newline

n \geq 1

n

\newline

n \geq 1

n

Margaret is writing a recursive function for the geometric sequence:

\newline

10,30,90,270, \ldots

\newline

She comes up with:

\newline

\left\{\begin{array}{l} t(0)=10 \\ t(n)=t(n-1) \cdot 3 \end{array}\right.

\newline

What domain should Margaret use for

t

so it generates the sequence?

\newline

1

\newline

n \geq 0

n

\newline

n \geq 0

n

\newline

n \geq 1

n

\newline

n \geq 1

n

Rosita is writing an explicit function for the geometric sequence:

\newline

80,40,20,10, \ldots

\newline

She comes up with

\newline

t(n)=160\left(\frac{1}{2}\right)^{n} \text {. }

\newline

What domain should Rosita use for

t

so it generates the sequence?

\newline

1

\newline

n \geq 0

n

\newline

n \geq 0

n

\newline

n \geq 1

n

\newline

n \geq 1

n

David is writing an explicit function for the arithmetic sequence:

\newline

10,13,16,19, \ldots

\newline

He comes up with

s(n)=7+3 n

\newline

What domain should David use for

s

so it generates the sequence?

\newline

1

\newline

n \geq 0

n

\newline

n \geq 0

n

\newline

n \geq 1

n

\newline

n \geq 1

n

\left\{\begin{array}{l}f(1)=-16 \\ f(n)=f(n-1) \cdot\left(-\frac{1}{2}\right)\end{array}\right.

\newline

f(3)=

\begin{array}{l}\left\{\begin{array}{l}f(1)=3 \\ f(n)=f(n-1)+5.5\end{array}\right. \\ f(3)=\square\end{array}

\begin{array}{l}\left\{\begin{array}{l}h(1)=-5 \\ h(n)=h(n-1)+1.8\end{array}\right. \\ h(3)=\square\end{array}

\begin{array}{l}\left\{\begin{array}{l}f(1)=-3 \\ f(n)=2 \cdot f(n-1)+1\end{array}\right. \\ f(2)=\square\end{array}

\begin{array}{l}\left\{\begin{array}{l}g(1)=50 \\ g(n)=8-g(n-1)\end{array}\right. \\ g(2)=\square\end{array}

\begin{array}{l}\left\{\begin{array}{l}f(1)=-3 \\ f(n)=-5 \cdot f(n-1)-7\end{array}\right. \\ f(2)=\square\end{array}

\begin{array}{l}\left\{\begin{array}{l}g(1)=4 \\ g(n)=g(n-1) \cdot(-3)\end{array}\right. \\ g(3)=\square\end{array}

\begin{array}{l}\left\{\begin{array}{l}g(1)=4 \\ g(2)=-3 \\ g(n)=g(n-2) \cdot g(n-1)\end{array}\right. \\ g(3)=\end{array}

\begin{array}{l}\left\{\begin{array}{l}g(1)=-5 \\ g(2)=3 \\ g(n)=g(n-2)+g(n-1)\end{array}\right. \\ g(3)=\square\end{array}

\begin{array}{l}\left\{\begin{array}{l}f(1)=-2 \\ f(2)=5 \\ f(n)=f(n-2) \cdot f(n-1)\end{array}\right. \\ f(3)=\end{array}

\begin{array}{l}\left\{\begin{array}{l}f(1)=-6 \\ f(2)=-4 \\ f(n)=f(n-2)+f(n-1)\end{array}\right. \\ f(3)=\end{array}

\begin{array}{l}\left\{\begin{array}{l}g(1)=0 \\ g(n)=g(n-1)+n\end{array}\right. \\ g(2)=\square\end{array}

\begin{array}{l}\left\{\begin{array}{l}f(1)=1 \\ f(2)=2 \\ f(n)=f(n-2)+f(n-1)\end{array}\right. \\ f(3)=\square\end{array}