All categories

3 years ago

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 geometric 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.

Examples

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

___

General Term

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.

Sum of Terms

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)

You might be interested in

Grasshoppers are distributed at random in a large field according to a Poisson process with parameter a 5 2 per square yard. How

HACTEHA [7]

In this question, the Poisson distribution is used.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

Parameter of 5.2 per square yard:

This means that $\mu = 5.2r$ , in which r is the radius.

How large should the radius R of a circular sampling region be taken so that the probability of finding at least one in the region equals 0.99?

We want:

$P(X \geq 1) = 1 - P(X = 0) = 0.99$

Thus:

$P(X = 0) = 1 - 0.99 = 0.01$

We have that:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-5.2r}*(5.2r)^{0}}{(0)!} = e^{-5.2r}$

Then

$e^{-5.2r} = 0.01$

$\ln{e^{-5.2r}} = \ln{0.01}$

$-5.2r = \ln{0.01}$

$r = -\frac{\ln{0.01}}{5.2}$

$r = 0.89$

Thus, the radius should be of at least 0.89.

Another example of a Poisson distribution is found at brainly.com/question/24098004

3 0

3 years ago

The endpoints of CD are C(−2, 0) and D(4, 9). The coordinates of the midpoint M of CD are?

jenyasd209 [6]

Answer:

1, 4.5

Step-by-step explanation:

for midpoint

x₁ = -2, y₁ = 0

x₂ = 4, y₂ = 9

for midpoint

(x₁+x₂)/2 , (y₁+y₂)/2

(-2+4)/2 , (0+9)/2

2/2 , 9/2

1, 4.5

4 0

2 years ago

Read 2 more answers

A bakery offers a sale price of $3.40 for 4 muffins. What is the price pe dozen?

maxonik [38]

Answer:

10.2

Step-by-step explanation:

3.40 * 3 = 10.2

5 0

2 years ago

How can 2/3 + 3/12 be rewritten so they can be added?

Drupady [299]

well, you can multiply the values to where they are equivalent, so multiply 2/3 by 4 ( both numbers ) so you get 8/12 and 3/12, so, just in case you want POST added, the answer to 2/3 ( 8/12 ) + 3/12 = is 11/12!

Hope this helps, if not, comment below please!!!

6 0

2 years ago

Read 2 more answers

Can someone please do this for me

Natasha_Volkova [10]

Next time please indicate which problem you want to work on.

One example of an equation with variables present on both sides is

y-b = m(x-a). Given the slope of a line and one point (a,b) through which the line passes, you can come up with an equation of the line.

Or, given the numeric value of y-b and that of x-a, you could obtain the slope of the line thru the points (x,y) and (a,b).

7 0

2 years ago