The sum of the fifth and sixth term of an AP is 30.If the third term is 5.Find the first term.

Answers

Answer 1

Answer:

The first term is -3.

Step-by-step explanation:

Arithmetic sequence:

In an arithmetic sequence, the difference between two consecutive terms is always the same, and it is called common difference d.

The nth term is given by:

[tex]a_n = a_1 + (n-1)d[/tex]

In which [tex]a_1[/tex] is the first term.

If we have the mth term instead of the first, we have:

[tex]a_n = a_m + (n-m)d[/tex]

We have the third term, and need the fifth and the sixth:

So we write both the fifth and the sixth in function of the third, then:

[tex]a_5 = a_3 + 2d = 5 + 2d[/tex]

[tex]a_6 = a_3 + 3d = 5 + 3d[/tex]

The sum of the fifth and sixth term of an AP is 30

We use this to find [tex]d[/tex]. So

[tex]a_5 + a_6 = 30[/tex]

[tex]5 + 2d + 5 + 3d = 30[/tex]

[tex]5d + 10 = 30[/tex]

[tex]5d = 20[/tex]

[tex]d = \frac{20}{5} = 4[/tex]

First term:

The third term is:

[tex]a_3 = a_1 + 2d[/tex]

Since [tex]a_3 = 5, d = 4[/tex]

[tex]a_1 = a_3 - 2d = 5 - 8 = -3[/tex]

The first term is -3.


Related Questions

Which of the following is(are) the solution(s) to |7x +12|= 12?
O A. x = -24,0
O B. x= 24,0
24
O C. X=-
O D. x = 0

Answers

Answer:

the answer is B because theres no negative

Round to the nearest hundredth (2 decimal places) when necessary

Answers

Answer:

216 is the area

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

if it's area, then:

area = 216 cm²

Step-by-step explanation:

area = 1/2bh = 1/2(27)(16) = 216 cm²

Pls help I give brainliest and pls get this right

Answers

It’s the last one, -2 and 1/3
Its the last one, -2 1/3 plus -5 would get -7 1/3

How many classes would Gina need to take for the total cost to be the same at both dance studios

Answers

Answer:

How many classes is Gina taking?

Answer:

10

Step-by-step explanation:

right on edge

Pls help Homework is due tomorrow and Im not sure about the answer!

Answers

Answer:

The picture isn't clear enough.

Help please this question is important!!!!

Answers

A = P(1 + r/n)^nt
p=2000
r=.052
n=4
t=8
answer is 3,023.66

The number of pets is shown for houses on four different streets. Which data set fits a normal distribution curve?
O 3, 5, 4, 3, 4, 5, 4, 3, 4, 5, 3, 4,3,4,5,4,5,5, 4,5
O 2, 1, 4, 5, 3, 2, 1, 2, 3, 5, 6, 4, 5, 2, 2, 3, 4, 5, 2,7
O 0,3, 4, 2, 1, 4, 0,5, 4, 6, 4, 3, 4, 2, 1, 5, 6, 4, 3,5
4, 7, 8, 9, 0, 6, 5, 6, 8, 7, 1, 2, 3, 4, 5,3,4,6,7,7

Answers

Answer:65454545

Step-by-step explanation:

???
Help ? ................

Answers

Answer:

A. [tex]\frac{9}{5}[/tex]

Step-by-step explanation:

-[tex]\frac{1}{4}[/tex] ( -[tex]\frac{4}{5}[/tex] / [tex]\frac{2}{3}[/tex] ) 6

Note that when dividing fractions, you can flip one and multiply instead to gte the same answer.

-[tex]\frac{1}{4}[/tex]*6( -[tex]\frac{4}{5}[/tex] * [tex]\frac{3}{2}[/tex] )

[tex]\frac{-6}{4}[/tex] ( [tex]\frac{-4*3}{5*2}[/tex] )

[tex]\frac{-6}{4}[/tex] ( [tex]\frac{-12}{10}[/tex] )

[tex]\frac{-6*-12}{4*10}[/tex]

[tex]\frac{72}{40}[/tex]

Divide top and bottom by 8.

[tex]\frac{72/8}{40/8}[/tex]

[tex]\frac{9}{5}[/tex]

i think it’s c. 4/5 sorry if i am wrong though

3.
Write the equation of the line best fit

Answers

Answer:

i dont quite have a answer i just need points sorry good luck tho .

put the answer in parenthesis please also solve in quadratic formula

Answers

Answer:

2(x+3)²+12=4

2x+6²+12=4

2x+36+12=4

2x=4-36-12

2x=-44

2x/2x=-44/2x

x=-22

A Sociology student investigated the association between a country's Literacy Rate and Life Expectancy, and then drew the conclusions listed below. Explain why each statement is incorrect. (Assume that all the calculations were done properly.)
a) The $$R^2$$ of 64% means that the Literacy Rate determines 64% of the Life Expectancy for a country.
b) The slope of the line shows that an increase of 5% in Literacy Rate will produce a 2-year improvement in Life Expectancy.

Answers

Solution :

The term 'literacy rate' provides the ability of a person who is from a definite age group can read or write.

a). [tex]$R^2$[/tex] does not determine the rate at which the variable explains another, but it explains the amount the amount of variability in one of the variables as explained by the other variable.

b). The slope given provides an expected improvement but it cannot guarantee the improvement. The value may be less or it could be more also.

The regression model provides the prediction and not the actual values.

The distance between the amusement park and the bus terminal on a map is 2.25 inches. The map uses a scale in which 1 inch represents 15 miles. What is the actual distance between the amusement park and the bus terminal?

Answers

Answer:

33.75 miles

Step-by-step explanation:

[tex]\frac{1}{15} :\frac{2.25}{y}[/tex]

1 × y = 2.25 × 15

y = 33.75

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Answers

Answer: b is the answer

Step-by-step explanation:

A math teacher at George Washington Middle School asked boys in the 6th and 7th grades to report their shoe size. She used the results to create these histograms

Which conclusion best supported by the histograms?
A as boys get older, shoe sizes become more normally distributed with fewer large outliers.
B As boys get older, shoe size range, defined by the minimum and maximum, decreases
C As boys get older, shoe sizes increase and the distribution remains relatively unchanged.
D As boys get older, shoe size distribution becomes more spread with more large outliers

Answers

Answer:

As boys gets older, shoe sizes becomes more normally distributed with fewer large outliers.

Step-by-step explanation:

A visual analysi ls of the histogram distribution provided, we can observe that size distribution of 6 graders is positively skewed (right tailed) as outliers seems more to the right(large sizes). However, the second graph is balanced with a normal or symmetric distribution representing older age (7th graders). Hence, we can conclude that as the boys gets older, they attain normality in terms of their shoe sizes. And the outliers which are characterized by the first histogram having vanished or reduced.

Answer plz I will make first correct answer brainleist

Answers

Answer:

18

Step-by-step explanation:

Jay had three cupcakes he divided the cupcakes by 1/3 how many pieces of cupcakes does Jay have now

Answers

Answer:

9

Step-by-step explanation:

if one cupcake is split into 3 pieces *1/3 per piece* then 3 cupcakes would be 9 slices in total *3x3=9*

what is the reciprocal of 453463.432849

Answers

Answer: 0.00000220524

Step-by-step explanation:

What's the right answer?

Answers

Given:

[tex]sinh(f(x))=1+x^2[/tex]

To find:

The value of f'(x).

Solution:

Formulae used:

[tex]\dfrac{d}{dx}sinh(x)=cosh(x)[/tex]

[tex]\dfrac{d}{dx}x^n=nx^{n-1}[/tex]

[tex]\dfrac{d}{dx}C=0[/tex]

Chain rule:

[tex]\dfrac{d}{dx}[f(g(x))]=f'(g(x))g'(x)[/tex]

Where C is an arbitrary constant.

We have,

[tex]sinh(f(x))=1+x^2[/tex]

Differentiate with respect to x.

[tex]cosh(f(x))f'(x)=0+2x[/tex]

[tex]f'(x)=\dfrac{2x}{cosh(f(x))}[/tex]

Therefore, the required values is [tex]f'(x)=\dfrac{2x}{cosh(f(x))}[/tex].

Melody's dad brought home a crate of apples he picked from their orchards. The crate contained 10 Granny Smiths, 14 Red Delicious, and 4 Golden Delicious. After replacing the first apple, she took out a second apple. What is the probability of picking a Golden Delicious and then a Granny Smith?​

Answers

i need the answer options

Step-by-step explanation:

NO LINKS!!! Find the measurement indicated. Round your answer to the nearest tenth.

Answers

Answer:

Solutions given;

Using cosine rule

b²=a²+c²-2*a*c*cos B°

b²=15²+8²-2*15*8*cos39

b²=102.48

b=[tex] \sqrt{102.48} [/tex]

b=10.12

b=10.1

Using sine rule

[tex] \frac{sin A}{BC} = \frac{sin B}{AC} =\frac{sin C}{AB} [/tex]

[tex] \frac{sin 29°}{15} =\frac{sin C}{8} [/tex]

Doing criss cross multiplication

Sin C=[tex] \frac{sin 29°}{15} ×8[/tex]

m<C=Sin -¹(0.29)

m<C=14.98

m<C=15°is a required answer.

Which set of ordered pairs is a function? {(1,1),(2, 2), (3, 3), (4,4), (5,5)} {(0,0),(1,1),(1, -1),(4,2),(4, -2)} {(2,1),(2,2).(2,3),(2,4),(2,5)} {(1,5).(2.4),(3,3).(2, 2), (1,1)​

Answers

[tex] \underline{ \underline{ \large{ \red{ \tt{✧ E\: X \: P \: L \: A \: N \: A \: T\: I \:O\: N}}}}} : [/tex]

❀ Here, We are given relation from A to B [ Suppose ] & We have to identify whether they are function or not from the relation A to B.

{ ( 1 , 1 ) , (2 , 2 ) , ( 3 , 3 ) , (4 , 4 ) , ( 5 , 5 )}

⇢ This is a function from A to B because every element of Set A has unique image in set B.

{( 0,0 ) , ( 1 , 1 ) , ( 1 , -1 ) , ( 4 , 2 ) , ( 4 , -2 ) }

⇢ This is not a function because two of the elements of Set A ( 1 & 4 ) are associated to elements -1 , 1 & 2 , -2 respectively of Set B

{ ( 2 , 1 ) , (2 , 2 ) , (2 , 3 ) , (2 , 4 ) , (2 , 5 )

⇢ This is not a function because the element of Set A ( 2 ) is associated to all the elements of Set B.

{ ( 1 , 5 ) , ( 2 , 4 ) , ( 3 , 3 ) , (2 , 2 ) , ( 1 , 1 )

⇢ This is not a function because the elements of Set A ( 1 & 2 ) are associated to elements ( 5 , 1 & 4 , 2 ) of Set B respectively.

[tex] \boxed{ \boxed{ \large{ \purple{ \tt{A \: N \: S \: W \: E \: R: \{ ( 1 , 1 ) , (2 , 2 ) , ( 3 , 3 ) , (4 , 4 ) , ( 5 , 5 ) \} }}}}}[/tex]

♨ Q. What is function ? How can we identify whether the given relation is a function ?

⟶Function is a special type of relation. Function is the refinement of relation. In a relation from A to B , every element of Set A has only one ( distinct ) image in B. In other words , if no two different ordered pairs have the same first component , then it is a function.

# STUDY TIP :

♕ Have a hard time memorising ?

Read it 10 times Say it 10 times Write it 2 times

ツ Hope I helped! ♡

✎ Let me know if you have any questions!

[tex] ♪ \underbrace{ \overbrace{ \mathfrak{Carry \: On \: Learning ☄}}}[/tex]

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Susan has a blue skirt, a green skirt, and a gray skirt. She also has a white sweater, a purple sweater, and a green sweater.
If she randomly selects her outfit, what is the probability she will select the gray skirt and the purple sweater to wear to work that day?

Answers

The answer is 1/9. The picture is the working out hope you have a great day :)

What is an angle that is adjacent to
CED?

Answers

i think BEA is adjacent to it

ONE HUNDRED POINTS PLEASE BE HONEST.

Answers

Answer:

12.207

Step-by-step explanation:

a^2 + b^2 = c^2

a and b are legs of the right triangle, c is the hypotenuse.

The hypotenuse squared is equal to the square root of (7^2 + 10^2).

The square root of 149 is around 12.207.

You cannot simplify the square root of 149 so if the question wants it in radical form just input square root of 149.

According to the preamble, who gives power to the
Constitution?


O foreign powers
O the people
O the states
O elected officials

Answers

the people

The Preamble of the Constitution states that the people of the United States are the ones who ordain and establish the Constitution to promote the general welfare. Therefore, the American people are the ones who give it power.

Answer:

The People

Step-by-step explanation:

The first part of the preamble states, "We the People of the United States, in Order to form a more perfect Union..." The United States government was built by the people, for the people. It was important to the founding fathers that there could be a democracy where the people could hold the power of the government. So, they wrote this into the constitution and preamble.

Round to the nearest hundredth (2 decimal places) when necessary

Answers

Answer:

148.92 is the area of the triangle

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

If it's area, then:

area = 148.92 in²

Step-by-step explanation:

area = 1/2(20.4)(14.6) = 148.92 in²

The area of a square floor on a scale drawing is 36 square centimeters, and the scale drawing is 1 centimeter:3 ft. What is the area of the actual floor? What is the ratio of the area in the drawing to the actual area?

Answers

Answer:

36 answer

Step-by-step explanation:

y=x−1
2x+y=8
If you were to solve the following system using substitution, your new equation would be...

Answers

Answer:

2x+ (x-1) = 8

Simplified

3x-1 =8

Step-by-step explanation:

y=x−1

2x+y=8

Take the first equation and everywhere you see y in the second equation substitute x-1

2x+ (x-1) = 8

You can simplify

2x+x-1 =8

3x-1 =8

If you want to solve

3x-1+1 =8+1

3x= 9

Divide by 3

3x/3 =9/3

x=1

Then solve for y

y = x-1

y = 3-1

y=2

WHATS THE EQUATION & TELL HOW YOU GOT IT !!


PLEASE HELP !! ILL GIVE BRAINLIEST!! 100 POINTS !! NO FAKE ANSWERS.


Answers

Answer: 3x+18=5x-2

Step-by-step explanation:

3x+ 18x=5x-2

(3x+18x)=5x-2

21x=5x-2

5x 5x

16x=-2

16. 16

X= -1/8

Indicate in standard form the equation of the line passing through the given point and having the given slope.
A(5,5), m=3

Answers

Answer:

-4,0  -4,0

Step-by-step explanation:

-4,0  -4,0

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