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Pachacha [2.7K]
3 years ago
11

Can someone explain what geometric sequences are?

Mathematics
1 answer:
Fed [463]3 years ago
8 0

Explanation:

A sequence is a list of numbers.

A <em>geometric</em> sequence is a list of numbers such that the ratio of each number to the one before it is the same. The common ratio can be any non-zero value.

<u>Examples</u>

  • 1, 2, 4, 8, ... common ratio is 2
  • 27, 9, 3, 1, ... common ratio is 1/3
  • 6, -24, 96, -384, ... common ratio is -4

___

<u>General Term</u>

Terms of a sequence are numbered starting with 1. We sometimes use the symbol a(n) or an to refer to the n-th term. The general term of a geometric sequence, a(n), can be described by the formula ...

  a(n) = a(1)×r^(n-1) . . . . . n-th term of a geometric sequence

where a(1) is the first term, and r is the common ratio. The above example sequences have the formulas ...

  • a(n) = 2^(n -1)
  • a(n) = 27×(1/3)^(n -1)
  • a(n) = 6×(-4)^(n -1)

You can see that these formulas are exponential in nature.

__

<u>Sum of Terms</u>

Another useful formula for geometric sequences is the formula for the sum of n terms.

  S(n) = a(1)×(r^n -1)/(r -1) . . . . . sum of n terms of a geometric sequence

When |r| < 1, the sum converges as n approaches infinity. The infinite sum is ...

  S = a(1)/(1-r)

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777dan777 [17]

♡ The Question ♡

-  -4(-3n-8)=104

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*

♡ The Answer ♡

-  D) 6

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*

♡ The Explanation/Step-By-Step ♡

-  -4(-3n - 8) = 104

Divide both sides by -4!

-4(-3n - 8) over -4 = 104/-4

Simplify!

-3n - 8 = -26

Add 8 to both sides!

-3n - 8 + 8 = -26 + 8

Simplify!

-3n = -18

Divide both sides by -3!

-3n/-3 = -18/-3

Simplify!

n = 6

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*

♡ Tips ♡

- No tips provided!

5 0
3 years ago
The area of a rectangular pool was 120square meters. If the long side in 7 meters plus a number and the width is 6 meters. What
NeX [460]

Answer:

The value of the variable=13 meters

Step-by-step explanation:

Step 1

Express the dimensions of the pool

Length=7+x

width=6

Step 2

Express the area of a rectangle as shown;

A=L×W

where;

A=area of a rectangle

L=length of the rectangle

W=width of the rectangle

In our case;

A=120 m²

L=x+7

W=6

replacing in the equation;

120 m²=(x+7)×6

120=6 x+42

6 x+42=120

6 x=120-42

6 x=78

x=78/6

x=13

The value of the variable=x=13 meters

8 0
3 years ago
What is the image point of (-1,-7) after a translation left 4 units and up 2 units?
bearhunter [10]

Step-by-step explanation:

hope this helps dear

it forms a right angle triangle I guess ☆☆

3 0
2 years ago
Differentiating Exponential Functions In Exercise, find the derivative of the function.<br> y = x2ex
I am Lyosha [343]

Answer:

y' = xe^{x}(2 + x)

Step-by-step explanation:

If we have a product function y, in the following format

y = f(x)*g(x)

This function has the following derivative

y' = f'(x)*g(x) + g'(x)*f(x)

In this problem, we have that:

y = x^{2}e^{x}

So

f(x) = x^{2}, f'(x) = 2x, g(x) = e^{x}, g'(x) = e^{x}

The derivative of the function is:

y' = f'(x)*g(x) + g'(x)*f(x)

y' = 2xe^{x} + x^{2}e^{x}

y' = e^{x}(2x + x^{2})

y' = xe^{x}(2 + x)

8 0
3 years ago
A cheetah ran 275 feet in 3.23 seconds. How fast did the cheetah run in miles per hour? Round your answer to the nearest whole m
yawa3891 [41]
First we convert feet into meters, since 1 feet is 0.3048 m: 275 feet * 0.3048 = 83.82m.

Then we do: 83.82m / 3.23s =  <span>25.9504644 m/s.

Then we convert that into miles per hour by </span>2.23694, so we do:

25.9504644 * 2.23694 = <span>58.0496318.

Then we round it to 58 mph.

So the answer is: The cheetah was running at 58 mph.

Hope this helped! c:</span>
6 0
3 years ago
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