Mathematics High School

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:

S_6 = 252

Step-by-step explanation:

We are told that the 10th, 4th and 1st term of an A.P are three consecutive terms of a G.P.

Now,formula for nth term of an AP is;

a_n = a + (n - 1)d

Thus;

a_10 = a + (10 - 1)d

a_10 = a + 9d

Also;

a_4 = a + (4 - 1)d

a_4 = a + 3d

First term is a.

Thus, since they are consecutive terms of a G.P, it means that;

(a + 9d)/(a + 3d) = (a + 3d)/a

Cross multiply to get;

a(a + 9d) = (a + 3d)(a + 3d)

a² + 9ad = a² + 6ad + 9d²

a² will cancel out to give;

9ad - 6ad = 9d²

3ad = 9d²

Divide both sides by 3d to get;

a = 3d

We are told that the first term is 4.

Thus, 4 = 3d

d = 4/3

We saw earlier that ratio of the GP is (a + 3d)/a

Thus; r = (4 + 3(4/3))/4 = 8/4 = 2

Sum of n terms of a G.P is given by;

S_n = a(rⁿ - 1)/(r - 1)

S_6 = 4(2^(6) - 1)/(2 - 1)

S_6 = 252

Related Questions

Pleaseee help answer correctly !!!!!!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!

Answers

Answer:

Step-by-step explanation:

is saving money to buy a game. So far he has saved $36, which is three-fourths of the total cost of the game. How much does the game cost?

PLS HELP ME IM GIVING 10 POINTS FOR THIS!

Answers

if $36 is 3/4 of the total cost, then you can divide 36 by 3 to get the answer for what 1/4 of the cost is. 36 divided by 3 is 12. 12 times 4 is 48. the cost is $48.

A ratio that compares a number to 100 is called a percent. True or False?

Answers

Answer:

True

Step-by-step explanation:

The statement "a ratio that compares a number to 100 is indeed called a percent" is true.

Percentages are used to express proportions or ratios out of 100. They are commonly denoted by the symbol "%."

Percentages provide a convenient way to represent fractions or parts of a whole in a standardized and easily understandable format.

For example, if a student scores 85 out of 100 on a test, it can be expressed as 85%, indicating that the student achieved 85 out of possible 100 marks.

Thus, the statement "a ratio that compares a number to 100 is indeed called a percent" is true.

Learn more about the percentages here:

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Plz help!

According to the graph, what are the domain and range of f(x)

Answers

Answer:

Domain: [0, 40]

Range: [0, 20]

General Formulas and Concepts:

Algebra I

Domain is the set of x-values that can be inputted into function f(x)Range is the set of y-values that are outputted by function f(x)Interval Notation - [a, b] denotes inclusive, (a, b) denotes exclusive

Step-by-step explanation:

According to the graph, we see that our x-values span from 0 to 40. Since both are closed dots, they are included in the domain:

Interval Notation [0, 40]

Inequality Notation 0 ≤ x ≤ 40

According to the graph, we see that our y-values span from 0 to 20. Since both are closed dots, they are included in the range:

Interval Notation [0, 20]

Inequality Notation 0 ≤ y ≤ 20

7W + 5 + 6 + 3w
Just help me pleAsee

Answers

Answer:

the answer is 10w + 11

Nijah has 45 stickers
she gives 2/5 to her sister and
the remaining 1/3 to brett

how many dose she have left ?

Answers

Answer: 6

Step-by-step explanation:

At Pete's pizza, the cost of a 1 topping pizza is $17.35 and the cost of a 3 topping pizza is $21.05.
Assuming the cost of a pizza follows a linear model, write an equation that represents C, the cost of any pizza with t,toppings.

Answers

Answer:

Step-by-step explanation:

17.35 * 3

Help!!Suppose f (x) = x-4. Find the graph of
3/4 f(x)

Answers

Answer:

Jcjdhdydifcjxjdfvb graph1

how many significant figures are in 2856.110

Answers

‍♀️‍♀️‍♀️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

5. There are three different colored M&Ms
red, green, and white. The probability of
selecting a red M&M is 2/5 and the probability
of selecting a green M&M is 1/4 so what is the
probability of selecting a white M&M?

Answers

The total number of red m&m out of all m&m is 2/5.

The total number of green m&m out of all m&m is 1/4.

if we add up 2/5 and 1/4, we can use that information to subtract from the total number of m&m to find the rest of m&m, which would be a total number of white m&m!

2/5 + 1/4 = ?

Common denominator. We will choose 20, since it is the lowest common multiple! (this means that 20/20 is the total number of all m&m, by the way. )

[tex]\frac{2(4)}{5(4)}[/tex] + [tex]\frac{1(5)}{4(5)}[/tex] = 8/20 + 5/20 = a

20/20 - a = ?

ANSWER: 7/20

The probability of selecting a white-colored M&M is 7/20.

The total number of red m&m out of all m&m is 2/5.

The total number of green m&m out of all m&m is 1/4.

if we add up 2/5 and 1/4, we can use that information to subtract from the total number of m&m to find the rest of m&m, which would be a total number of white m&m

2/5 + 1/4 = ?

Common denominator. We will choose 20, since it is the lowest common multiple (this means that 20/20 is the total number of all m&m, by the way. )

What is the probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

8/10 +5/20 = 8/20 + 5/20 = a

20/20 - a = ?

Therefore the probability of selecting a white M&M is 7/20.

To learn more about probability visit:

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I need help due tmmr

Answers

Answer: C.

Step-by-step explanation:

The answer is C. i believe

Answer:

food : 22

clothes : 48

Step-by-step explanation:

70 - 26 = 44

44 divided by 2 = 22

22 + 26 = 48

70 - 48 = 22

New York and Chicago are 4 inches apart on a map if the scale on a map is 1/2 inch equal 100 miles how many miles is it from New York to Chicago

Answers

800 miles
1 inch equal 200 miles

what is the length of line segment FH?

Answers

Answer:

19 is the answer

Step-by-step explanation:

15+4=19

Answer:

Hi how are you doing today Jasmine

Solve the equations: √y^6=-y^3

Answers

Answer:

√y^6=-y^3

y^6/2=-y^3

y^3+y^3=1

2y^3=1

y^3=1/2

[tex] \sqrt[3]{1 \div 2 } [/tex]

Lol helpppppppp meee plsssss!!!!

Answers

Answer:

83.3%

Step-by-step explanation:

5/6~=0.833

which is 83.3%

Jada and Priya are trying to solve the equation 2/3+x=4
Jada says, “I think we should multiply each side by 3/2 because that is the reciprocal of 2/3."
Priya says, “I think we should add -2/3 to each side because that is the opposite of 2/3."
1. Which person's strategy should they use?
2. Explain your reasoning.

Answers

Answer:

Priya is correct. Because 2/3 is being added to x and not multiplied, then subtracting 2/3 from both sides is the correct action.

Step-by-step explanation:

Let's run through solving it that way:

2/3 + x = 4

2/3 - 2/3 + x = 4 - 2/3

0 + x = 4 - 2/3

x = 4 - 2/3

x = 10/3

Please answer quick!
Which segment is the image of Line segment A B reflected across the line y = negative 2?

On a coordinate plane, segment A B goes from (2, negative 7) to (8, negative 3), segment J K goes from (2, 7) to (8, 3), segment G H goes from (2, 3) to (8, negative 1), segment F A goes from (negative 4, negative 3) to (2, negative 7), and C D goes from (negative 8, negative 3) to (negative 2, negative 7).

A.)Line segment A F
B.)Line segment D C
C.)Line segment G H
D.)Line segment J K

X = 6
9/12 = 0.75
6/8 = 0.75

What is 5/3+2/4= ????

Answers

Answer:

5/3 x 4/4

2/4x 3/3

20+6/12

26/12

Step-by-step explanation:

Answer:

the answer is

5/3+2/4=7/4

One angle of an isosceles triangle measures 26°. Which other angles could be in that isosceles triangle?

Answers

Answer:

There are two answers, either of which would work

26°, 26° and 128°26°, 77° and 77°

Method:

An isosceles triangle has 2 of the same sides so there are two possible answers:

1) 26° is one of the angles which is the same as another. 26° × 2 = 52° and since there are 180° in a triangle the other angle is 180° - 52° which is 128°. This would make the angles 26°, 26° and 128°

2) 26° is not one of the angles which is the same as another. Since there are 180° in a triangle, the other angles would both be 2 ÷ (180° - 26°) which is 77°. This would make the angless 26°, 77° and 77°

I will give Brainliest !

Answers

Answer:i believe it’s A

Step-by-step explanation:

4,5,3 are almost the same and almost the same rotation just letters are different

4. Jake wants to make a garden with a border in the corner of his yard. He has lumber in several different lengths. Which three lengths could NOT be used to make a right triangle to fit into the corner of his yard? O 5 ft., 12 ft., 13 ft. O 9 ft., 12 ft., 15 ft. O 16 ft., 12 ft., 20 ft. 0 0 O 10 ft., 12 ft., 15 ft.

Answers

Answer:

10 ft., 12 ft., 15 ft.

Step-by-step explanation:

Note that for a right triangle, the sum of the square of the hypotenuse is equal to the sum of square of the opposite and the adjacent.

Note that the hypotenuse is the longest side

Checking the given sides 10 ft., 12 ft., 15 ft.

Hypotenuse = 15ft (longest side)

Take the square of 15

15² = 225

Take the sum of square of other two sides

12²+10²

= 144 + 100

= 244

Since 225≠244, hence the three length could not be used to make a right triangle to fit into the corner of his yard

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