Express the following relationship as a rate.

What is the explicit formula for this sequence?<br><br> −7, −4, −1, 2, 5, …

VikaD [51]

The explicit formula for the sequence is 3n -10

<h3>What is an Arithmetic Sequence ?</h3>

An arithmetic sequence is a series of terms which have common difference between its consecutive numbers.

The sequence given is

−7, −4, −1, 2, 5, …

The common difference between each term is d =3

-4-(-7) = 3

-1-(-4) =3

The nth term for a sequence is given by

$\rm T_n = a +(n-1)d$

Here a is the first term = -7

n is the no. of terms = n

d is the common difference = 3

Therefore the equation will be

$\rm T _n = -7 + (n-1) * 3$

$\rm T _n$ = -7 +3n -3

$\rm T _n$ = 3n -10

Therefore the explicit formula for the sequence is 3n -10 .

To know more about Arithmetic Sequence

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7 0

2 years ago

SOMEONE ANSWER THESE PLEASE!!

Svetradugi [14.3K]

Answer:
1). Because whole number doesn’t allow decimal numbers.

2). Because whole number doesn’t allow negative numbers. It starts with 0, 1, 2, 3....

7 0

3 years ago

An Archer shoots an arrow horizontally at 250 feet per second. The bullseye on the target and the arrow are initially at the sam

Genrish500 [490]

Answer:

Step-by-step explanation:

Using the formula for finding range in projectile, Since range is the distance covered in the horizontal direction;

Range $R = U\sqrt{\frac{H}{g} }$

U is the velocity of the arrow

H is the maximum height reached = distance below the bullseye reached by the arrow.

R is the horizontal distance covered i.e the distance of the target from the archer.

g is the acceleration due to gravity.

Given R = 60ft, U = 250ft/s, g = 32ft/s H = ?

On substitution,

$60 = 250\sqrt{\frac{H}{32}} \\\frac{60}{250} = \sqrt{\frac{H}{32}}\\\frac{6}{25} = \sqrt{\frac{H}{32}$

Squaring both sides we have;

$(\frac{6}{25} )^{2} = (\sqrt{\frac{H}{32} } )^{2} \\\frac{36}{625} = \frac{H}{32} \\625H = 36*32\\H = \frac{36*32}{625} \\H = 1.84feet$

The arrow will hit the target 1.84feet below the bullseye.

5 0

3 years ago

Erik and Caleb were trying to solve the equation: 0=(3x+2)(x-4) Erik said, "The right-hand side is factored, so I'll use the zer

Mumz [18]

Answer:

C) Both

Step-by-step explanation:

The given equation is:

$0=(3x+2)(x-4)$

To solve the given equation, we can use the Zero Product Property according to which if the product <em>A.B = 0</em>, then either A = 0 OR B = 0.

Using this property:

$(3x+2) = 0 \Rightarrow \bold{x = -\frac{2}{3}}\\(x-4) = 0 \Rightarrow \bold{x = 4}$

So, Erik's solution strategy would work.

Now, let us discuss about Caleb's solution strategy:

Multiply $(3x+2)(x-4)$ i.e. $3x^2-12x+2x-8$ = $3x^2-10x-8$

So, the equation becomes:

$0=3x^2-10x-8$

Comparing this equation to standard quadratic equation:

$ax^2+bx+c=0$

a = 3, b = -10, c = -8

So, this can be solved using the quadratic formula.

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\dfrac{-(-10)\pm\sqrt{(-10)^2-4\times3 \times (-8)}}{2\times 3}\\x=\dfrac{-(-10)\pm\sqrt{196}}{6}\\x=\dfrac{10\pm14}{6} \\\Rightarrow x= 4, -\dfrac{2}{3}$