3.
If the second and the seventh terms of a geometric progression are 6 and 1458
respectively, find the first term.

Answers

Answer 1

Answer:

steps below

Step-by-step explanation:

aₙ = a₁ * rⁿ⁻¹

a₁ * r²⁻¹ = 6

a₁ * r = 6   ... (1)

a₁ * r⁵ = 1458  ... (2)

(2)/(1) : r⁴ = 243      r = ±3 [tex]\sqrt[4]{3\\}[/tex]

if r = 3 [tex]\sqrt[4]{3\\}[/tex]

[tex]a_{1} = 6 / 3\sqrt[4]{3} \\a_{1} = \frac{2}{3} \sqrt[4]{27}[/tex]  

if r = -3 [tex]\sqrt[4]{3\\}[/tex]

[tex]a_{1} = -\frac{2}{3} \sqrt[4]{27}[/tex]

Answer 2

The first term of the geometric progression is 256.

What is a geometric sequence?

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

We have,

Let the first term of the geometric progression be denoted by 'a', and let the common ratio be denoted by 'r'.

According to the problem, the second term is 6, so we have:

ar = 6 ...(1)

Similarly, the seventh term is 1458, so we have:

[tex]ar^6[/tex] = 1458 ...(2)

We can use equation (1) to solve for 'r', and then substitute the value of 'r' into equation (2) to solve for 'a'.

From equation (1), we have:

r = 6/a

Substituting this into equation (2), we get:

[tex]a(6/a)^6[/tex] = 1458

Simplifying the right side of the equation, we have:

[tex]6^6[/tex] = 1458a

Solving for 'a', we get:

a = [tex]6^6[/tex]/1458 = 256

Therefore,

The first term of the geometric progression is 256.

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Related Questions

Roman numerals for 29 is​

Answers

hello!

Answer:

XXIX

Step-by-step explanation:

Hope this helps! :)

A speaker is in the shape of a cube with an edge length of 3.5 inches. The speaker is sold in a package in the shape of a square prism with a base area of 16 in2 and a height of 4.25 inches. What is the surface area of the package

Answers

Step-by-step explanation:

A square prism is a three-dimensional cuboid where the base and top are equal squares and the remaining 4 faces are rectangles.

to get the surface area of the package (that square prism) the size of the content inside is irrelevant and only there to confuse us.

the package has a base area of 16 in².

that means it also has a top (or cover) area of the same size : 16 in².

as top and bottom are squares, that means their areas are the square of their side lengths.

therefore, the side length of such a square is

s = sqrt(16) = 4 in

now we know also the dimensions of the 4 rectangles that are the side areas (faces) : 4 in × 4.25 in

the area of such a rectangle is

4 × 4.25 = 17 in²

so, the total surface area is (top and bottom + 4 side areas)

2×16 + 4×17 = 32 + 68 = 100 in²

Select the two roots of (3x+7)(2x-5)=0
A= -7/3
B= 5/2
C= -5/2
D= 7/3

Thank you

Answers

Given

(3x + 7)(2x - 5) = 0

Equate each factor to zero and solve for x

3x + 7 = 0 ⇒ 3x = - 7 ⇒ x = - \frac{7}{3}

3\7

→ A

2x - 5 = 0 ⇒ 2x = 5 ⇒ x = \frac{5}{2}

2\5

→ B

PLEASE HELPPP!
assume the random variable X has a by normal distribution with the given probability of obtaining a success.  find the following probabilities, given the number of trials in the probability of obtaining a success. P(X < 5), n = 6, p = 0.7

Answers

Answer:

-7

Step-by-step explanation:

Question is attached.
Step by step explanation only!​

Answers

Answer:

Attached is your answer.

Step-by-step explanation:

hence Proved.

Hope it helps you!!

LHS

[tex]\\ \sf\longmapsto \dfrac{cos(90-\Theta)}{sin\Theta}+\dfrac{sin\Theta}{cos(90-\Theta)}[/tex]

[tex]\boxed{\sf cos(90-A)=sinA}[/tex]

[tex]\\ \sf\longmapsto \dfrac{sin\Theta}{sin\Theta}+\dfrac{sin\Theta}{sin\Theta}[/tex]

[tex]\\ \sf\longmapsto 1+1[/tex]

[tex]\\ \sf\longmapsto 2[/tex]

Hence proved

the quotient of a number less than 8 and 5​

Answers

x - 8/5 will be your answer. Remember the entire numerator is divided by 5!

Answer:

8/5

Step-by-step explanation:

Write
17/3
as a mixed number.
O A. 3
O-B. 3
© C.53
O D. 53

Answers

Answer:

5 2/3

Step-by-step explanation:

15 ÷ 3 = 5.

with 2 leftover, you will have 2/3

5 + 2/3 = 5 2/3

Good Luck!

-kiniwih426

Answer:

I am not really sure about the answer choices, but the answer is 5 2/3

Step-by-step explanation:

17/3 - 3/3 = 1 14/3

14/3 - 3/3 = 2 11/3

11/3 - 3/3 = 3 8/3

8/3 - 3/3 = 4 5/3

5/3 - 3/3 = 5 2/3

Hopefully this helped!

Brainliest please?

3) At a school several teachers were holding a contest to see which class could earn the most trivia points. Mrs. Clawson's class scored 94 points. Mr. Grant's class earned 82 points. Mrs. Jones's class earned 94 and Mrs.Price's class earned 86. Determine the mean (rounded to the nearest tenth), median, mode and range of the number of points scored. Mean: Median: Mode: Range:​

Answers

Answer:

Mean: 89

Median: 90

Mode: 94

Range: 12

What is the answer please

Answers

Answer:

-2 < x < 4.5

Step-by-step explanation:

Step 1: Add 1 to all parts/sections.

[tex]-5+1<2x-1+1<8+1[/tex] [tex]-4<2x<9[/tex]

Step 2: Divide all parts/sections by 2.

[tex]\frac{-4}{2}<\frac{2x}{2} <\frac{9}{2}[/tex] [tex]-2 < x < 4.5[/tex]

Therefore, the range of possible values of x is -2 < x < 4.5.


1. One species of bamboo can grow at an average rate
of 60 centimeters per day. Assuming that the
bamboo plant maintains the average rate of
growth per day, how tall will the bamboo plant be
if it grows for:
a. 10 days?

b. 30 days?

c. one-half day?

Show step by step please

Answers

A: 600 Centimeters
Reason: 60c x 10 days = 600c

B:
1800 centimeters
Reason 60c x 30 days = 1800c

C:
30 centimeters
Reason: 60c x .5 = 30c
.5=12 hours
1.5=36 hours

Find the value of x that makes m ∥ n.

Geometry: CC 2015 > Chapter 3: Proofs with Parallel Lines > Section Exercises 3.3

Answers

Answer:

X = 23∘

 

Step-by-step explanation:

(

7

x

11

)

=

(

4

x

+

58

)

 corresponding angles are always equal.

3

x= 69

x = 69

3 = 23

There are 20% more goblins than wizards in magic club. There are 220 goblins and wizards together in magic club. How many goblins are in magic club ?

Answers

Answer:

120

Step-by-step explanation:

w = wizards

1.2w = goblins

_________

w + 1.2w = 220

2.2w = 220

w = 100

This means there are 100 wizards. To find the number of goblins just plug the number of wizards in the goblins = 1.2w.

1.2 (100) = 120.

There are 120 goblins in the magic club.

A pair of parallel lines cut by a transversal as shown. Which of the following best represents the relationship between angles p and q?

A. p = 180 degrees - q
B. q = 180 degrees - p
C. p = 2q
D. p = q​

Answers

D. P=Q
Since they are alternating exterior angles, they have the same measurement.

Answer:

p=q is the right answer...

Help this is due today

Answers

Answer:

The answer is 19/12

Step-by-step explanation:

Hope this helped

The answer is 3/4 to your problem

In triangle, ABC, sin A = 1/2b =20,and m

Answers

Answer:

here your answer

good luck

HELLOOO HELPPPPPPPPPP

Answers

Answer:

the answer to this question is 2/5

Highest common factor of 42,72,and 56

Answers

Answer:

the HCF is 2

Step-by-step explanation:

Write the equation for the function graphed below.

Answers

Given the vertex of the parabola at point (2, -3):

The quadratic function in vertex form is:

f(x) = (x - 2)^2 - 3

where the vertex (h, k) is the minimum point = (2, -3).

The equation of the function graphed below is f(x) = a(x - 2)² - 3 since the vertex is at (2, -3).

We have,

From the graph given,

The vertex is at (2, -3).

Now,

The vertex form of a quadratic function is given by:

f(x) = a(x - h)² + k

Where (h, k) is the vertex of the parabola.

Given the vertex (2, -3), we can plug in the values of h and k into the vertex form:

f(x) = a(x - 2)² - 3

Thus,

The equation of the function graphed below is f(x) = a(x - 2)² - 3

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Adding Unlike denominators 1/11 + 1/4

Answers

Answer: 15/44

Step-by-step explanation:

You have to make the denominators match so:

1/11(4) + 1/4(11)=

4/44 + 11/44=

15/44

Un empresario compró 1000 tabletas a $1500 cada una. Vendió 450 de ellas obteniendo una
ganancia del 25%.
¿ A qué precio deberá vender las otras 550 restantes si la utilidad promedio del lote completodebe ser del 40%?

Answers

Answer:

Step-by-step explanation:

1000($1500(0.40)) = $600 000

450($1500(0.25)) = $168,750

600,000 - 168,750 = $431,250

$431,250 / 550 = 784.0909090... $784.09

$1500 + $784.09 = $2,284.09

12 + 4x > 24 or 10 - 12x > 22

Answers

Answer:

10 - 12 × > 22 Yan Yong sagot

A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 higher than in the first. The tax in the first city was
3.5%, and the tax in the second city was 5%. The total hotel tax paid for the two cities was $386.25. How much was the hotel charge in each city before tax?
First city:
Х
SLU
Second city: 0
5
?.

Answers

This is your answer
Please mark as a brilliant

Use the given property to complete the statement.
Distributive Property

3(x-1)= 3x - ?

A) -1

B) -3

C) 1

D) 3

Answers

Answer:

B) -3

Step-by-step explanation:

Use distributive property.

3(x-1)(3*x) - (3*1)3x - 3

3(x-1) = 3x - 3

Hence, it is verified that choice B) -3 is the correct answer.

Simplity -4/3 ➗2/-6
-4
-2
2
4
I

Answers

Answer:

-4

Step-by-step explanation:

-4/3÷2/-6

⇒ -4/3×-6/2

⇒ -24/6

⇒ -4

PLS HELP ME 100 POINTS AND FIRST TO ANSWER GETS BRAINLIEST
Which arrangement shows −512 , −5 , −6.4 , and −264 in order from least to greatest? −264, −6.4, −5, −512 −512 , −6.4 , −264 , −5 −512 , −5 , −264 , −6.4 −264, −6.4, −512, −5

Answers

Answer:

-512, -264, -6.4, -5

Step-by-step explanation:

Since we need to go from least to largest, you would use the order above.

The order from least to greatest is -512, -264, -6.4, -5.

The given integers are −512, −5, −6.4 and −264.

What is ascending order of negative integers?

Ascending order of negative numbers means to arrange the given negative numbers from smallest to largest values.

It is very important to learn as in the case of negative numbers the absolute values of smaller numbers are greater than the absolute values of larger numbers, which makes it confusing.

Now, ascending order of given negative integers is as follows:

-512 < -264 < -6.4 < -5

So, the order from least to greatest is -512, -264, -6.4, -5.

Therefore, the order from least to greatest is -512, -264, -6.4, -5.

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Shamika's grandmother opens an account with a deposit of $5,000 for Shamika as a
college savings account. The account pays 5 percent annual interest. How much
money will be in the account after 10 years?

A. 8,954.24

B. 8,144.47

C. 8,052.55

D. 7,401.22

Answers

9514 1404 393

Answer:

  B.  $8,144.47

Step-by-step explanation:

The compound interest formula is ...

  A = P(1 +r)^t

where r is the annual rate compounded annually for t years, applied to principal P.

  A = $5000(1 +0.05)^10 = $8144.47

After 10 years, there will be $8,144.47 in the account.

Test: Chapter 1-4 Test
Is 9 a solution to the equation x+2=x+2?
Yes
No

Answers

Answer:

Yes..............

....

.

Please answer the question in the picture

Answers

Answer:

f(x)=2x+1

Step-by-step explanation:

gradient =(y2-y1)/(x2-x1)

(3-1)/(1-0)

=2

y=1

David is making a model of a regular triangular prism.
Calculate the surface area of the prism.
__ inches squared

Answers

108.18 inches squared

1/2(4.2 x 4.5) = 9.45
9.45 x 2 = 18.9

4.5 x 4.2 = 18.9

6.3 x 6.3 = 39.69
39.69 x 2 = 79.38

18.9 + 18.9 + 79.38 = 108.18

18,234.9+516.1 show your work

Answers

Answer:

18,751

Step-by-step explanation:

18 234 . 9

516 . 1

----------------

18 751 . 0

----------------

Answer:

18,751

Step-by-step explanation:

18,234.9+516.1=18,751

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