The 10th, 4th and 1st term of an A.P are three consecutive find the common ratio of the G.P and the sum of the 6th term, taking the 1st term to be 4

Answers

Answer 1

Answer:

Common ratio=1/2

Sum of first 6 terms of an A.P=31.5

Step-by-step explanation:

Let a be the first term and d be the common difference of an A.P

a=4

nth term of an A.P

[tex]a_n=a+(n-1)d[/tex]

Using the formula

[tex]a_4=a+3d=4+3d[/tex]

[tex]a_{10}=a+9d=4+9d[/tex]

According to question

We know that

For G.P

[tex]\frac{a_n}{a_{n-1}}=r[/tex]=Common ratio

[tex]r=\frac{4+3d}{4+9d}=\frac{4}{4+3d}[/tex]

[tex]\frac{4+3d}{4+9d}=\frac{4}{4+3d}[/tex]

[tex](4+3d)^2=\frac{4}{4+3d}[/tex]

[tex]16+9d^2+24d=16+36d[/tex]

[tex]9d^2+24d-36d-16+16=0[/tex]

[tex]9d^2-12d=0[/tex]

[tex]3d(3d-4)=0[/tex]

[tex]d=0, d=4/3[/tex]

Substitute the value of d

When d=0

[tex]r=\frac{4}{4+3d}=\frac{4}{4+0}=1[/tex]

When d=4/3

[tex]r=\frac{4}{4+3\times \frac{4}{3}}=\frac{1}{2}[/tex]

But we reject d=0 because  if we take d=0 then the terms are not consecutive terms of G.P

Sum of n terms of an A.P

[tex]S_n=\frac{n}{2}(2a+(n-1)d)[/tex]

Using the formula

Substitute n=6 and d=1/2

[tex]S_6=\frac{6}{2}(2(4)+5\times \frac{1}{2})[/tex]

[tex]S_6=31.5[/tex]


Related Questions

Please help!!! I’m stuck

Answers

Answer:

20/29

Step-by-step explanation:

Since 20inches is the opposite side size to the angle. Opposite = 20.

[tex] \cos( \alpha ) = \frac{adj}{hyp} [/tex]

Note: Hypothenus is the longest side of a right angle triangle which is 29inches.

Thus,

[tex] \cos( \alpha ) = \frac{20}{29} [/tex]



Tamara feeds her cat 1/8cup canned food each day and the

rest dry. She also gives her cat one treat a day. How much

dry food does Tamara feed her cat in a week? 3/8 cup of per day

4. MP.2 Reasoning What quantities are given in the problem

and what do the numbers describe?

cup of food pes

5. MP.1 Make Sense and Persevere What do you need

to find?

Answers

Do not copy Faroquem9’s work I just used it to answer your question and also I just used it as a example and wrote it on my own way so don’t copy it use it as a example and write it on your own way or answer it on your own way

AND THIS IS NOT MY WORK IT IS Faroquem9’s work..

Two consecutive integers do the the square root 45 lies​

Answers

Answer:

square root 45 lies between 6 and 7

Step-by-step explanation:

I hope it's helpful!

Answer:

6 and 7

Step-by-step explanation:

Consider the perfect squares on either side of 45, that is

36 < 45 < 49 , then

[tex]\sqrt{36}[/tex] < [tex]\sqrt{45}[/tex] < [tex]\sqrt{49}[/tex] , that is

6 < [tex]\sqrt{45}[/tex] < 7

help me 20 points, please

Answers

Thanks but have to go

which is the simplified form of the expression 3(7/5x+4) - 2(3/2 - 5/4x)?
A. -39/5x - 11/2
B. 67/10x + 9
C. 3/10x + 5/2
D. 15 + 76/10x

Answers

Answer:

B. [tex]\frac{67}{10} x + 9[/tex]

Step-by-step explanation:

Simplify the expression. Remember to go by the order of operations, or PEMDAS.

1) First, distribute the numbers outside of the set of parentheses to the terms inside the set of parentheses next to them. Then, simplify the fractions.

[tex]3(\frac{7}{5} x + 4) -2 (\frac{3}{2} -\frac{5}{4} x)[/tex]

[tex]\frac{21}{5}x + 12 - \frac{6}{2} + \frac{10}{4} x[/tex]

[tex]\frac{21}{5} x + 12 - 3 + \frac{10}{4} x[/tex]

2) Finally, combine like terms. (This means to add or subtract constants and to add or subtract terms with the same variables.) You may need to convert terms to the same denominator in order to do so easier. Then, reduce the fraction.

[tex]\frac{21}{5} x + 9 + \frac{10}{4}x \\\frac{84}{20}x + \frac{50}{20}x + 9 \\\frac{134}{20}x + 9 \\\frac{67}{10}x + 9[/tex]

Thus, the answer is [tex]\frac{67}{10} x + 9[/tex].

Answer:

B. 67/10x + 9

Step-by-step explanation:

Help? Please? And make sure the answer is right plz!! :) and have a good day

Answers

Answer:

-7

Step-by-step explanation:

The amount of degrees would be the same in both those corner/angle/section are. and have a good day as well!

-11 2/3 x (-4 1/5) HELPPPP!!!

Answers

Answer:

49

Step-by-step explanation:

(−11 2/3)(−4 1/5)

=  (-35/3) (-21/5)

= 49

Hope I helped!!

Plz help me I need a good person to help plz plz

Answers

Answer:

True

Step-by-step explanation:

Thhe answer to this is true

hey saben cuanto es -2x+2x es que me confundo mucho

Answers

-2x+2x=0
que pasen buen día

What's the circumference of a
circle with a diameter of 31 inches?
Use 3.14 for pi.

Answers

Answer:

circumference = 97.34

Step-by-step explanation:

circumference = diameter x Pi

31 x 3.14 = 97.34 inches

The circumference of the circle with a diameter of 31 inches is approximately 97.34 inches.

The circumference of a circle can be calculated using the formula C = πd, where C represents the circumference and d represents the diameter of the circle.

Given that the diameter of the circle is 31 inches, we can substitute this value into the formula:

C = 3.14 * 31

C ≈ 97.34 inches

Therefore, the circumference of the circle with a diameter of 31 inches is approximately 97.34 inches.

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Charolette is running at a rate of 9km/h. What is Charolette’s speed in m/s?

Answers

Answer:

seems like the main concept being tested here is unit conversion.

First, let's look at converting kilometers to meters. In the metric system, the prefix "kilo" means 1000. So,

1 kilometer = 1000 meters.

Then, let's look at converting from hours to seconds. As you may know, there are 60 minutes in an hour, and 60 seconds in a minute. So, in 1 hour there are

1 hour*(60 minutes/hour)*(60 seconds/minute) = 3600 seconds.

So, we can use these unit conversion factors to solve your question. Let's convert the units!

9 km/hr = 9 km/hr * (1000 m/km) * (1 hr/ 3600 sec) = 2.5 m/s

Hope this helps!

Step-by-step explanation:

Answer:

2.5m/s

Step-by-step explanation:

The sail on a souvenir boat is similar in shape to the sail on a sailboat. The sail on the sailboat is in the shape of a right triangle with a base of 9 feet and height of 24 feet. The height of the souvenir's sail is 3 inches. What is the base of the souvenir's sail

Answers

Answer:

1 1/8 inches.

Step-by-step explanation:

As the sails are similar,  corresponding sides are in the same ratio, so we have the equation

:24/3 = 9/b     where  b = base of the souvenir boat.

Cross multiply:

24b = 9*3

b = 27/24

= 1 1/8 inches.

Based on the shape of the souvenir and dimensions of boat, the base of the souvenir's sail is 1.125 inches

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

WE need to find the base of the souvenir sail.

Given that sail on the souvenir boat has the same shape as the sail on the sailboat. Which means that; they can be used to find each other's dimensions based on a scale factor.

The height of the sailboat = 24 feet.

The height of the souvenir boat's sail = 3 inches.

The scale is:

= 24 / 3

= 8

Then for every inch on the souvenir boat's sail, the sailboat is 8 feet.

The base of the souvenir boat sail;

= 9 / 8

= 1.125 inches

Hence, Based on the shape of the souvenir and dimensions of boat, the base of the souvenir's sail is 1.125 inches

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Hans opens a circular window that is 3.5 feet across at its widest point. What is the circumference of the window to the nearest whole number? Use 3.14 for π. help pls

Answers

Answer: 11

Step-by-step explanation:

i did 3.5 x 3.14 = 10.99 and rounded to the nearest whole number, 11.

The circumference of the circular window to the nearest whole number is 11 feet.

What is a circle?

A circle is a two-dimensional figure with a radius and circumference of 2pir.

The area of a circle is pir^2.

We have,

To find the circumference of the circular window, we need to use the formula:

C = πd

where C is the circumference, π is the constant pi, and d is the diameter of the circle.

Since the window is 3.5 feet across at its widest point, the diameter of the circle is also 3.5 feet.

Plugging in the value of the diameter in the formula, we get:

C = πd

C = 3.14 x 3.5

C = 10.99

Rounding the result to the nearest whole number, we get:

C ≈ 11 feet

Therefore,

The circumference of the circular window to the nearest whole number is 11 feet.

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Q: Simplify.

1. 3^(n+1) - 3^n / 3^(n-1)​

Answers

Answer:

3^(n+1) - 3^n / 3^(n-1)​ = 6

16. Jason purchased a used vehicle that depreciates under a straight-line method. The initial value of the car is $5000, and the salvage value is $500. If the car is expected to have a useful life of another 5 years, what will its value be in 1 year?​

Answers

Answer

1,500? I think any way.

Step-by-step explanation:

5,000 divided by 5 = 1,000

1,000 + 500 = 1,500

Answer:

1,500

Step-by-step explanation:

and jeez the other kid was just having fun

A piece of ribbon is 1 metre in length. Sasha cuts of some of the
ribbon. The ribbon is now 40 cm in length.
What is the percentage change of the ribbon?

Answers

Answer:

high jatdog

Step-by-step explanation:

napaka pogi ko ayieeee

how many solutions does x=-2 have

Answers

Answer:

One solution

Step-by-step explanation:

In a one- variable equation has infinitely many solutions when solving results in a true statement, such as 2=2

In a one- variable equation has one solution when solving results in one value for the variable, such as x = 5

In a one - variable equation has no solution when solving results in an untrue statement, such as 2=3

So, in this case the result x = -2 belongs to the 2nd sentence where it says one solution.

Hope this helps :)

In a family expenditure on food and education are in the ratio3:5.If expenditure education is Rs7000, find the expenditure on food.​

Answers

Answer:

3×7000:5×X

21000:5X

so X= 4200

So expenditure on food will be Rs4200

-12x2 – 16x
Help me with this please

Answers

Answer:

-4x(3x+4)

Step-by-step explanation:

You have to undo the problem, I will show you how this problem looks if you solve it (the answer i guess? id.k it is hard to explain any other way)

So first we use distributive property-

-4x *3x=-12x^2

-4x*4=-16x

-12x^2-16x  And now we have the problem we started with!

Answer:

its -4x(3x+4)

Step-by-step explanation:

can someone please help me

Answers

x equals to eight probably

simplify √-48


-4√3

4√-3

4i√3

4√3i

Answers

Answer:

√-48=4i√3

Step-by-step explanation:

because negative number never has a real root so 1st and 2nd option r out . i^2= -1 so root and Square cuts out eachother so i should be out of the root hence option 4th is also cut out. so 3 rd is correct.

C would be the best choice for the question :)

If MNOP is an isosceles trapezoid, MP = 16x - 13, NO = 9x + 8, PN = 5y + 19, and
MO = 12y - 37
What is the measure of segment NP?

Answers

Answer:

59

Step-by-step explanation:

The diagonals of an isosceles trapezoid are equal.

MO and NP are diagonals.  Therefore MO = NP

12y - 37 = 5y + 19

7y = 56

y = 8

MO = 12(8) - 37 = 96 - 37 = 59

NP = 5(8) + 19 = 40 + 19 = 59

7 units are the measurement of the segment NP.

What is a polygon?

In Mathematics, a polygon can be defined as a two-dimensional geometric figure that consists of straight line segments and a finite number of sides. Additionally, some examples of a polygon include the following:

• Triangle

• Quadrilateral

• Pentagon

• Hexagon

• Heptagon

• Octagon

• Nonagon

Generally speaking, the measure of the angle at the center of a regular polygon is equal to 360 degrees. Therefore, the smallest angle of rotation that maps (carries) a regular polygon onto itself can be calculated by using this formula:

α = 360/n

Since MNOP is an isosceles trapezoid, the non-parallel sides MN and OP have the same length. Therefore, we can set up an equation using the given lengths of the sides:

MP = NO

Substituting the given expressions for these lengths, we get:

16x - 13 = 9x + 8 + 5y + 19

Simplifying and rearranging terms, we get:

7x - 5y = 36 ........(1)

Similarly, we can set up another equation using the given lengths of the diagonals MO and PN:

MO + PN = MP + NO

Substituting the given expressions for these lengths, we get:

12y - 37 + 5y + 19 = 16x - 13 + 9x + 8

Simplifying and rearranging terms, we get:

17y - 16x = 42 ........(2)

Now, we have two equations (1) and (2) with two variables (x and y). Solving this system of equations, we get:

x = 7, y = 9

Substituting these values back into the given expressions for PN and NO, we get:

PN = 5y + 19 = 5(9) + 19 = 64

NO = 9x + 8 = 9(7) + 8 = 71

Therefore, the measure of segment NP is:

NP = NO - PN = 71 - 64 = 7

So, the measure of segment NP is 7 units.

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In 2001, 229 million cartons of apples were produced in the U.S. If 40% of the apples were eaten as fresh fruit, how many apples were used for fruit juice and other things?

Answers

We can say with certainty 2.29M is 1%. 2.29*40=91.6M

So 229M-91.6M=137.4M
137,400,000 Apples for other things other than consumption.

5m+2n-7-2m+15 Simplified expression

Answers

5m+2n-7-2m+15

Combine all like terms.

3m+2n+8

What is 11 divided by 5 as a fraction

Answers

It’s like 22/10 or something

11 divided by 5 is equal to the fraction 11/5, which can also be expressed as the mixed number [tex]2\frac{1}{5}[/tex] .

What is 11 divided by 5 as a fraction?

To convert the division of 11 by 5 into a fraction, we can express it as a ratio of two integers. Here's how we can derive the fraction:

When we divide 11 by 5, we get a quotient of 2 with a remainder of 1. So, we can write the division as:

11 ÷ 5 = 2 + 1/5

Since 2 is a whole number, we can express it as a fraction with a denominator of 1:

2 = 2/1

Now, we can rewrite the division using the same denominator:

11/5 = 2/1 + 1/5

To combine the fractions, we need a common denominator. The least common multiple (LCM) of 1 and 5 is 5. Therefore, we can multiply the fractions by appropriate values to make their denominators equal to 5:

11/5 = (2/1) × (5/5) + (1/5) = 10/5 + 1/5

Now that the denominators are the same, we can add the fractions:

11/5 = (10 + 1)/5 = 11/5

Therefore, the division of 11 by 5 can be expressed as the fraction 11/5.

The fraction 11/5 represents the result of dividing 11 into 5 equal parts. Each part would be equal to 11/5. It can also be simplified to a mixed number as 2 1/5, where the whole number part is 2 and the fractional part is 1/5.

So, 11 divided by 5 is equal to the fraction 11/5, which can also be expressed as the mixed number 2 1/5.

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...............................

Answers

Answer: Graphing is the best in this situation

Step-by-step explanation:

Function or not a function?

Answers

Answer:

Function

Step-by-step explanation:

(-2,2)(-1,2)(0,0)(1,-2)(2,1) the x does not repeat so it is a function

I also really need help with this question.

Answers

Answer:

The answer would be -12

Step-by-step explanation:

I hope this helps! Have an awesome day.

Answer:

-12

Step-by-step explanation:

Conver mixed number fractions into inproper fractions

[tex]\frac{-11}{2} - \frac{37}{4} + \frac{11}{4}[/tex]

Set common dinominators

[tex]\frac{-22}{4} - \frac{37}{4} + \frac{11}{4}[/tex]

Simplify

[tex]\frac{-48}{4}[/tex] = -12

find the measure of this angle in the triangle

PLEASE HELP this is the last question and im having trouble solving it!

I-ready

Answers

Answer:

85.....?................

when the cube root of a positive number “n” is squared, the result is 5, what is the value of “n”?

A) 2.9
B) 3.8
C) 11.2
D) 25.0
E) 42.7

type out explanation for brainliest :)

Answers

(n^1/3)^2 = n^3/2=5
(n^3/2)^2/3=5^2/3
n=5^2/3
n=2.9
A is the correct one

Answer:

A)2.9 is the value of "n".

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