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Anna11 [10]
3 years ago
5

What is the 6th term of the geometric sequence 4, −20, 100, ...?

Mathematics
2 answers:
shtirl [24]3 years ago
3 0
Let's calculate r of this G.P: (-20)/(4) = - 5(100)/(-20) = - 5So r = -5
The formula to find the nth term of a GP is;
a(n) = a(r)ⁿ⁻¹
<u />a₆ = a(r)⁶⁻¹
a₆ = 4(-5)⁵ = -12500<u />
Umnica [9.8K]3 years ago
3 0

Answer:

the 6th term of the given sequence is, - 12500

Step-by-step explanation:

The nth term for the geometric sequence is given by:

a_n = a_1 \cdot r^{n-1}      ....[1]

where,

a_1 is the first term

r is the common ratio of the terms.

Given the sequence:

4, −20, 100, ...

This is a geometric sequence.

Here,

a_1 =4 and r = -5

We have to find the 6th term of the given sequence:

Substitute n= 6 and the given values in [1] we have;

a_6 = 4 \cdot (-5)^5 = 4 \cdot -3125 = -12500

therefore, the 6th term of the given sequence is, - 12500

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a salesperson sells $2700 in merchandise and earns a commission of $351 what is the commission rate in percentages?
GaryK [48]

Answer:

Commision rate 13%

Explanation:

The commission rate is equal to the commission as a percent of sells.

Now in our case,

sells = $2700

commission = $351

Therefore, the commission rate is equal to

undefined

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1 year ago
Need help on this!!!!
Alexxandr [17]

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It's the first one.

Step-by-step explanation:

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<span>35g5 – 25g2 = 5g2(7g3 – 5) </span>⇒ should be: 35g⁵ - 25g² = 5g²(7g³ - 5) TRUE

Question 4. Completely factored.
16y⁵ + 12y³ = 4y³(4y² + 3) FACTORED COMPLETELY
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4 years ago
S squared minus y cubed
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s^2 - y^3

8 0
3 years ago
») What is the volume of a ball with adiameter of 6 centimeters? Use 3.14for (pie)How is the volume of a sphere related tothe vo
Dahasolnce [82]
Volume of a sphere and a cone

We have that the equation of the volume of a sphere is given by:

V=\frac{4}{3}\pi r^3

We have that the radius of a sphere is half the diameter of it:

Then, the radius of this sphere is

r = 6cm/2 = 3cm

<h2>Finding the volume of a sphere</h2>

We replace r by 3 in the equation:

\begin{gathered} V=\frac{4}{3}\pi r^3 \\ \downarrow \\ V=\frac{4}{3}\pi\cdot3^3 \end{gathered}

Since 3³ = 3 · 3 · 3 = 27

\begin{gathered} V=\frac{4}{3}\pi3^3 \\ \downarrow \\ V=\frac{4}{3}\pi\cdot27 \end{gathered}

If we use π = 3.14:

\begin{gathered} V=\frac{4}{3}\pi\cdot27 \\ \downarrow \\ V=\frac{4}{3}\cdot3.14\cdot27 \\ \downarrow \\ V=4.18\bar{6}\cdot27 \end{gathered}

Rounding the first factor to the nearest hundredth (two digits after the decimal), we have:

4.18666... ≅ 4.19

Then, we have that:

\begin{gathered} V=\frac{4}{3}\pi\cdot27 \\ \downarrow \\ V=4.19\cdot27 \\ =113.13 \end{gathered}

Then, we have that:

<h2>Finding the volume of a cone</h2>

We have that the volume of a cone is given by:

V=\frac{1}{3}\pi r^2h

where r is the radius of its base and h is the height:

Then, in this case

r = 3

h = 6

and

π = 3.14

Replacing in the equation for the volume:

\begin{gathered} V=\frac{1}{3}\pi r^2h \\ \downarrow \\ V=\frac{1}{3}\cdot3.14\cdot3^2\cdot6 \end{gathered}

Then, we have:

3² = 9

\begin{gathered} V=\frac{1}{3}\cdot3.14\cdot3^2\cdot6 \\ \downarrow \\ V=\frac{1}{3}\cdot3.14\cdot9\cdot6 \\ V=\frac{1}{3}\cdot3.14\cdot54 \\ V=56.52 \\  \end{gathered}

Answer: the volume of the cone that has the same circular base and height is 56.52 cm³

5 0
1 year ago
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