for the following geometric sequence find the explicit formula. {12, -6, 3, ...}​

Answers

Answer 1

Answer:

It's geometric sequence where a_1=12, q=-\dfrac{1}{2}a

1

=12,q=−

2

1

So a_n=12\cdot\left(-\dfrac{1}{2}\right)^{n-1}a

n

=12⋅(−

2

1

)

n−1

Answer 2

Answer:

[tex]a_{n}[/tex] = 12 [tex](-\frac{1}{2}) ^{n-1}[/tex]

Step-by-step explanation:

The nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Here a₁ = 12 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-6}{12}[/tex] = - [tex]\frac{1}{2}[/tex] , then

[tex]a_{n}[/tex] = 12 [tex](-\frac{1}{2}) ^{n-1}[/tex] ← explicit formula


Related Questions

In a group 40% like football ,70% like cricket and 30% like both games

Answers

Answer:

15% for both games

Step-by-step explanation:

30%÷2=15%

Which is the solution to the inequality below?
1x + 2 + 5 4
0 -3 < x < -1
no solution
O x < -3
O x > -1 or x < 3

Answers

Answer:

ox,-3

Step-by-step explanation:

Evaluate (y - 9) + (3 + x), when y = 15 and x = 5

Answers

Hi ;-)

[tex]y=15 \ and \ x=5\\\\(y-9)+(3+x)=(15-9)+(3+5)=6+8=\boxed{14}[/tex]

Answer:

14

Step-by-step explanation:

(y-9)+(3+x)

(15-9)+(3+5)

6+8

14

which expressionis equivalentto 83,100 in expand formusing power of 10?​

Answers

Answer:

8.3100 x [tex]10^{4}[/tex]

Explanation:

83100 in this form would be 8.3100 x [tex]10^{4}[/tex] because you can see 4 digits after the decimal point which would be raised to the 4th power of 10.

what is
[tex] \frac{28}{141} [/tex]
as a percentage​

Answers

The answer to the question is 17.02

Answer:

19,86%

Step-by-step explanation:

[tex] \frac{28}{141} = 0.198582[/tex]

➡️ [tex]0.1986[/tex]

➡️ [tex]0.1986 \times \frac{100}{100} [/tex]

➡️ [tex] \frac{0.1986 \times 100}{100} [/tex]

➡️ [tex] \frac{19.86}{100} [/tex]

➡️ [tex] = 19.86\%[/tex] ✅

suppose an object traveling in a straight line has a velocity function given by v(t)= t^2 -8t+ 15 km/hr. Find the displacement and distance traveled by the object from t=2 to t=4 hours.

Answers

v=t^2-8t+15

It has upper limit 4 and lower limit 2

[tex]\boxed{\sf {\displaystyle{\int}^b_a}x^ndx=\left[\dfrac{x^{n+1}}{n+1}\right]^b_a}[/tex]

[tex]\\ \sf\longmapsto s={\displaystyle{\int}}vdt[/tex]

[tex]\\ \sf\longmapsto s={\displaystyle{\int^4_2}}t^2-8t+15[/tex]

[tex]\\ \sf\longmapsto s=\left[\dfrac{t^3}{3}-8\dfrac{t^2}{2}+15t\right]^4_2[/tex]

[tex]\\ \sf\longmapsto s=\left[\dfrac{t^3}{3}-4t^2+15t\right]^4_2[/tex]

[tex]\\ \sf\longmapsto s=\left(\dfrac{4^3}{3}-4(4)^2+15(4)\right)-\left(\dfrac{2^3}{3}-4(2)^2+15(2)\right)[/tex]

[tex]\\ \sf\longmapsto s=\left(\dfrac{64}{3}-64+60\right)-\left(\dfrac{8}{3}-16+30\right)[/tex]

[tex]\\ \sf\longmapsto s=\left(\dfrac{64}{3}-4\right)-\left(\dfrac{8}{3}+14\right)[/tex]

[tex]\\ \sf\longmapsto s=\dfrac{64}{3}-4-\dfrac{8}{3}-14[/tex]

[tex]\\ \sf\longmapsto s=\dfrac{64}{3}-\dfrac{8}{3}-4-14[/tex]

[tex]\\ \sf\longmapsto s=\dfrac{46}{3}-18[/tex]

[tex]\\ \sf\longmapsto s=15.3-18[/tex]

Take it +ve

[tex]\\ \sf\longmapsto s=|-2.7|[/tex]

[tex]\\ \sf\longmapsto s=2.7km[/tex]

Type the correct answer in the box. Round your answer to the nearest hour. A scientist running an experiment starts with 100 bacteria cells. These bacteria double their population every 15 hours. Find how long it takes for the bacteria cells to increase to 300. Use the formula , where is the original number of bacteria cells, is the number after t hours, and d is the time taken to double the number. It takes 15 hours for the number of bacteria to increase to 300.

Answers

Answer:

so 15 hour for the 100 to become 200 and then it will become 400 in another 15 hours. but we need to find the time for 300 so it will take half of 15 hours

+ 15 hours for it to become 300 cells which is: 7 1/2 + 15 = 22 hours and 30 minutes

Step-by-step explanation:

answer from gauth math

Answer:

22 hours and 30 minutes

Step-by-step explanation:

if M∠ ABD =64 and M∠CBD=30 then M∠ABC=
Need help

Answers

Answer:

[tex]\displaystyle m\angle ABC = 34^\circ[/tex]

Step-by-step explanation:

∠ABD is the sum of the angles ∠ABC and ∠CBD. In other words:

[tex]\displaystyle m\angle ABD = m\angle ABC + m\angle CBD[/tex]

Substitute in known values:

[tex]\displaystyle \left(64^\circ\right) = m\angle ABC + \left(30^\circ\right)[/tex]

And subtract. Hence:

[tex]\displaystyle m\angle ABC = 34^\circ[/tex]

In conclusion, ∠ABC measures 34°.

3) What type of correlation would temperature
and ice cubes have?

Answers

temperature causes ice cubes to melt, or stay in the same state- temperature can impact state of matter in water, making ice cubes at 0 degrees Celsius

i’ll give brainliest pls
i need to finish this quickly, i need part a b and c

Answers

B 54

C 70

I got it right

How do you solve by undoing for 4-2x-x=12 in Algebra 1​

Answers

Hi ;-)

[tex]4-2x-x=12\\\\-2x-x=12-4\\\\-3x=8 \ \ /:(-3)\\\\x=-\frac{8}{3}=-2\frac{1}{3}[/tex]

7-15
Dividing decimals

Answers

Answer:

7-15= -8

Step-by-step explanation:

7-15= -8
so therefore the other person is correct

The sixth grade teachers bought food for a reward party. They purchased 64 bags of chips and 80 bottles of water . What is the largest number of students that can be invited to the party so they each get the same amount of chips and water?

Answers

Answer:

64

Step-by-step explanation:

Since each student must get the same amount of chips and water, the ratio of the number of chips to water received by each student is 1:1.

Hence, a maximum of 64 students can be invited to the party, as the bags of chips is lower than that of the number of bottles of water, and we take it as a 64.

Which one of the following statements must be true about the kite shown?
A. AB ≅ CB

B. BD ≅ AC

C. CD≅ BC

D)

Answers

Answer:

answer is Afridi.AB=CB

The unit circle with center at the origin is a relation but not a function. Find the two functions which are lie in one of the semicircle in part a, and determine their domains and ranges?

Answers

Answer:

Step-by-step explanation:

All real number

Reading - Word - Level 1
Vocabulary
Page 21
*
Safety is the number one priority at our trampoline parks.
That's why every session is supervised by our trained staff.
However, we cannot do it alone. We ask that parents and
guardians make sure their children follow our rules.
Informative
Persuasive

Answers

Answer:

crisp, clean, formal, readable

Step-by-step explanation:

Informative - that’s why every session is supervised by our trained staff

Persuasive - safety is number one

Pls give me a brainliest thx

PLS HELPP , i tried solving this and i wrote 56 but it was wrong so i don’t know anymore pls pls help

Answers

Answer:

y = 68

A = 44

Step-by-step explanation:

No matter what may be true, that doesn't look like an a to me.

x = y = 68                x and y are opposite equal sides and are therefore =.

68 + 68 + A = 180  all triangles are 180 degrees.

136 + A = 180          Subtract 136 from both sides

A = 180 - 136

A = 44

NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!

Water flows out of a hose at a constant rate. After 2 1/3 minutes, 9 4/5 gallons of water have come out of the hose. At what rate, in gallons per minute, is water flowing out of the hose?

Answers

Time taken:  2[tex]\frac{1}{3}[/tex] minutes = 7/3 minutes

Water released: 9[tex]\frac{4}{5}[/tex] gallons = 49/5 gallons

Rate of water flowing out:

Rate(in gallons/minute) = Water released (in gallons) / Time Taken (in minutes)

plugging the given values

Rate = [tex]\frac{\frac{49}{5} }{\frac{7}{3} }[/tex] = [tex]\frac{49}{5} * \frac{3}{7}[/tex]

Rate = 21/5 = 4.2 gallons/minute

Answer:

Time taken: 2\frac{1}{3}

3

1

minutes = 7/3 minutes

Water released: 9\frac{4}{5}

5

4

gallons = 49/5 gallons

Rate of water flowing out:

Rate(in gallons/minute) = Water released (in gallons) / Time Taken (in minutes)

plugging the given values

Rate = \frac{\frac{49}{5} }{\frac{7}{3} }

3

7

5

49

= \frac{49}{5} * \frac{3}{7}

5

49

7

3

Rate = 21/5 = 4.2 gallons/minute

Step-by-step explanation:

i hope it helps

Help me please! What shape is it?

Answers

it is a square has 4 equal sides and a pentagon has 5 so the answer is


SQUARE

You're a square !!!1!!!!!!!!11

In the Cartesian coordinate system, the x-akis is horizontal.

A.True
B. False

Answers

Answer:

A. True

Step-by-step explanation:

In the Cartesian coordinate system, the x-axis is the horizontal line while y-axis is the parallel line.

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

Is the product of a rational number and an irrational number always irrational?

Answers

Answer:

The product of any rational number and any irrational number will always be an irrational number.

Step-by-step explanation:

PLssssssss helppppppppppppppppppppppp

Answers

Answer:

6 ft

Step-by-step explanation:

ans all these questions please​

Answers

Answer:

Explanation:

a). 7(2x - 3)
= 7(2(4) - 3)
= 7(8 - 3)
= 35

b). (x + y)^2 - 3x
= (4 + 3)^2 - 3(4)
= 49 - 12
= 37

a). 2x x y
= 2(26) x 3b^2
= 52 x 3b^2
= 156b^2

b). mn/k
= 5a^5b x 4ab^3/10a^4b^3
= 20a^6b^3/10a^4b^3
= 2a^2

Answer:

the answer is in picture

3 3/5 divided by 1/6?

Answers

Answer:

10.8

Step-by-step explanation:

3 3/5 divided by 1/6

(3(3/5))/(1/6)

(9/5)/(1/6)

54/5

10(4/5)

10.8

Find all points on the x-axis that are 14 units from the point (5, -7)

Answers

Answer:

can you submit the coordinet plane?

Step-by-step explanation:


The shaded rectangle, which is the correct expression of its perimeter

Answers

Answer:

2x + 2y - 4

Step-by-step explanation:

The opposite sides are congruent so perimeter (P) is

P = 2(x + 2) + 2(y - 4)

  = 2x + 4 + 2y - 8

  = 2x + 2y - 4

(6, -1) translate
8 units to the right 7 units down

Answers

Step-by-step explanation:

স্বদেশী আন্দোলনৰ তিনি টা অৱদান উল্লেখ কৰা

Answer:

(14,-8)

Step-by-step explanation:

Given (6,-1),

Translating (6,-1) 8 units right and 7 units down,

(6,-1)

=(6+8,-1-7)

=(14,-8)

Please mark brainliest.

After subtracting 20% of a number from a number we get 12975.what was the number?​

Answers

Answer:

Step-by-step explanation:

d

the height of each door on the plan is given 1,5cm but the height of each door is 1,92m is an actual size.show that the scale of the house is 1:128​

Answers

Answer:

It is.

Step-by-step explanation:

1.5cm is in the plan.

1.92m is in real life.

We need to convert m to cm so 1.92m=192cm

The ratio is 1:128.

1.5cm in plan as is 192 cm in real life.We write that as the ratio of: 1.5 : 192.

We need to prove that it is the actual scale so we equal this ratio(1.5:192) and the other ratio(1:128):

1.5 : 192 = 1 : 128

Then we multiply the numbers that are in and out of the equation like this:

1.5 * 128 = 192 * 1

192 = 192 It is proven beacuse the numbers are equal. The scale of the house is 1:128

[tex]7w+2=3w+94[/tex]

Answers

Answer:

7w+2=3w+94

Subtract 3w from both sides.

7w+2−3w=94

Combine 7w and −3w to get 4w.

4w+2=94

Subtract 2 from both sides.

4w=94−2

Subtract 2 from 94 to get 92.

4w=92

Divide both sides by 4.

w=492

Divide 92 by 4 to get 23.

w=23

Answer:

23

Step-by-step explanation:

7w + 2 = 3w + 94                      Subtract 2 from both sides

7w = 3w + 94 - 2

7w = 3w + 92                             Subtract 3w from both sides

4w = 92                                      Divide by 4

w = 92/4

w = 23

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