the first and last term arithmetic sequence are 9 and 165 respectively.if the sum of all the terms of the arithmetic sequence is 3480,find the number of terms and the common difference of this arithmetic sequence​

Answers

Answer 1

Answer:

40 terms

Step-by-step explanation:

Sum of n terms formula:

Sn = 1/2n(a1 + an)

Solving for n

3480 = 1/2n(9 + 165)3480 = 87nn = 3480/87n = 40
Answer 2

Answer:

Required Answer:-first term =a=9Last term =l=165 Sn=3480

As we know that in a AP

[tex]{:}\longrightarrow[/tex][tex]\sf S_n={\dfrac {1}{2}}(a+l)n[/tex]

Substitute the values

[tex]{:}\longrightarrow[/tex][tex]\sf 3480={\dfrac {1}{2}} (9+165)n[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf 3480={\dfrac {1}{2}}(174)n[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf 3480={\dfrac {174}{2}}n [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf 3480=87n [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf n={\dfrac {3480}{87}}[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf n=40[/tex]

[tex]\therefore[/tex]Number of terms=40.


Related Questions

Witch atom has 12 protons

A carbon (C)
B nitrogen (N)
C sodium (Na)
D magnesium (Mg)

Also I didn’t mean to click a answer on there

Answers

magnesium! if you ever need anything else just ask!

Harriet used the work below to determine the percent equivalent to One-eighth.

Step 1: One-eighth = StartFraction question mark Over 100 EndFraction
Step 2: 8 divided by 100 = 0.08
Step 3: 0.08 times 1 = 0.08
Step 4: 0.08 percent

What was Harriet’s error?
In Step 1, she set up the proportions incorrectly.
In Step 2, she divided 8 by 100 instead of 100 by 8, so she cannot multiply the numerator by the factor.
In Step 3, she multiplied the numerator instead of the denominator by the factor.
In Step 4, she forgot to move the decimal.

Answers

Answer:

B

Step-by-step explanation:

Answer: B

Step-by-step explanation: It's B

Please help please help

Answers

Answer:

Do Y divided by X.

Step-by-step explanation:

This is normally what I do so hope I helped.

Where would -(-3) be on a number line?

Answers

it would be positive on the number line because a double negative is a positive so it would be at 3

what function best models the data and what wil be the chicken breast after 50 miutes​

Answers

Answer:

Students use linear, quadratic, and exponential functions to model data from tables and choose the regression

most appropriate to a given context. They use the correlation coefficient to determine the accuracy of a

regression model and then interpret the function in context. They then make predictions based on their model

and use an appropriate level of precision for reporting results and solutions.  

Lesson 7 focuses on data sets that cannot be modeled accurately, and students are asked

to articulate why. Students use skills learned in Lesson 14 of Module 2 (where they used

calculators to write linear regressions) and apply similar techniques for data sets that are

better suited to modeling with quadratic or exponential regressions. Students use that

same technique to find linear regressions and use their graphing calculators to examine

the correlation coefficient and to find quadratic and exponential regressions. They

compare correlation coefficients to determine which model is best for the data.

Ultimately, students choose the regression model (linear, quadratic, or exponential) most

appropriate to a given data set and then write, verify, and interpret these models in

context. Students need a graphing calculator to complete this lesson. Graphing calculator

instructions are provided, but steps may vary slightly depending on the model of the

graphing calculator.

Refer to the following full modeling cycle during this lesson (Found on page 61 of the CCLS

and page 72 of the CCSSM).

Scaffolding:

 Students are more

engaged when working

with relevant and real data

that interests them.

Websites that provide

data sets are a good

resource for classroom

investigations.

 This lesson might need to

be divided into two days if

students need more time

to master the technology.

Step-by-step explanation:

Solve the equation.
3/4x+3-2x=-1/4+1/2x+5

Answers

Answer:

x=-1

Isolate the variable by dividing each side by factors that dont

contain the variable

Dan and Paul share some money in the ratio 9:5.
Dan decides this is unfair so he gives Paul £32 of his share to make the ratio 1:1.
How much did Paul originally have?

Answers

Answer:

Paul had £40 originally.

Step-by-step explanation:

Given

Let d be the money Dan has and p be the money Paul has

Then according to the given situation,

[tex]\frac{d}{p} = \frac{9}{5}\\d = \frac{9p}{5}\ \ \ Equation\ 1[/tex]

Now from the statement, "Dan decides this is unfair so he gives Paul £32 of his share to make the ratio 1:1"

[tex]\frac{d-32}{p} = 1[/tex]     Eqn 2

From 2

[tex]d - 32 = p\\[/tex]

Putting d = 9p/5

[tex]\frac{9p}{5} - 32 = p\\9p - 160 = 5p\\9p-5p = 160\\4p = 160\\\frac{4p}{4} = \frac{160}{4}\\p = 40[/tex]

Checking

[tex]d = \frac{9(40)}{5} = \frac{360}{5} = 72\\\frac{d}{p} = \frac{72}{40} = \frac{9}{5}[/tex]

Hence,

Paul had £40 originally.

Estimate the:
length of a pen
length of a swimming pool
length of a marathon race​

Answers

Answers for question:

length of a pen:

5.2 inches 13.12 cm

length of a swimming pool:

50m

length of a marathon race:

42.195 kilometers

hope this answers your question!

I need help
With this please

Answers

Answer:

Ima be straight up with you im 1 awnser away from getting 50 points but ill find the answer for ya

Step-by-step explanation:

Solve four and six eighths minus two and three fifths.

(GIVING EXTRA POINTS AND GIVING BRAINLIEST!!)

A) one and six thirteenths

B) one and three fortieths

C) two and six fortieths

D) two and three thirteens

(Here is an image if needed) :

Answers

Answer:

I am not really sure but I asume it is C honestly I am sorry if I am wrong. But if I am right I really hope this helps

Matt has started a car washing business to save money for college. Each week, he
washes 3 more cars than he did the week before.

Answers

Answer:

Since this equation is not complete, I will just give an example.

Step-by-step explanation:

Lets say Matt starts out with 6 cars in week one. For the next week, just add the number 3 to the preexisting number (6), which will give you 9. Now, lets say he washes cars for 10 weeks to save money. All you would have to do is add a 3 each time to the preexisting number. So, it would go 6, 9, 12, 15, 18, 21, 24, 27 30, 33. The answer to the equation I created above is 33. I hope this helps you solve your question.

1. Francisco invested $5,000 into an account that earns 3% compounded quarterly. How many
times will Francisco earn interest after keeping the money in the account for 5 years?

2. What will be the value of his account in 5 years if he does not make any additional deposits or
withdrawals?

3. After how many years will Francisco’s account reach $10,000

4. If Francisco wanted to double his money in 12 years, what Interest rate would his account have to earn?

Answers

Answer:

10,002.21

Step-by-step explanation:

1)4x5= 20 times

2) principal= 5000

interest rate per year= 3%

compounded times per year=4

time in years = 5

the formula is amt= p*(1+r/n)^(n*t)

thus

Amount = 5805.92

3) If time in years = 23.2

then

amount = 10,002.56

4) Principal = 5,000

interest rate per yr= 5.82%

Compounded times per year = 4

time in years =12

Compute 41, 42, 43, 44, 45, 46, 47, and 48. Make a conjecture about the units digit of 4n where n is a positive integer. Use strong mathematical induction to prove your conjecture.

Answers

Answer:

The conjecture is that the unit digit of 4^n = 4 when n = odd also 4^n = 6 when n = even

Step-by-step explanation:

[tex]4^1 = 4\\4^2 = 16\\4^3 = 64\\4^4 = 256 \\4^5 = 1024\\4^6 = 4096\\4^7 = 16384\\4^8 = 65536[/tex]

The conjecture is that the unit digit of 4^n = 4 when n = odd also 4^n = 6 when n = even

To prove this conjecture

[tex]4^1 = 4\\4^2 = 16[/tex] unit digit = 6

hence the property is true for ; n = 1 and n = 2 and also for every odd and even number ( i.e. from 1  to 8 )

If AABC = ADEC,
ZB = 48° and ZE = x + 4

Answers

Answer:

[tex]x = 44^\circ[/tex]

Step-by-step explanation:

Triangle Congruence

Given triangle ABC is congruent to triangle DEC, then it's true that angle ABC is congruent to angle DEC.

The figure shows that:

[tex]m\angle B = 48^\circ[/tex]

[tex]m\angle E = x + 4^\circ[/tex]

Those angles are congruent, or have the same measure, thus:

[tex]x + 4^\circ = 48^\circ[/tex]

Subtracting 4°:

[tex]x = 48^\circ - 4^\circ[/tex]

[tex]\mathbf{x = 44^\circ}[/tex]

A triangle has sides with lengths 4.15, 7.092 and 12.45. What is the perimeter of the triangle?​

Answers

Answer:

Perimeter = 23.692 units

Step-by-step explanation:

Perimeter = sum of all his sides

then:

Perimeter = 4.15 + 7.092 + 12.45

Perimeter =  23.692 units

EASY QUESTION WILL GIVE BRAINLIEST!!!
Tyler has a baseball bat that weighs 28 ounces.
Find this weight in kilograms and in grams. (Note: 1 kilogram 35 ounces).
Make a table

Answers

Kilograms- .794
Grams- 793.787

9. A kitchen sink holds 24 gallons of water. A full sink drains at 3 gallons per minute. Which of
the following tables best represents the situation?
A.
Х
1
2
3
4
B.
Х
1
2
3
4
Y
24
48
72
96
Y
21
18
15
12
C.
Х
0
2
4
6
D.
Х
1
2
3
4
Y
24
21
18
15
Y
24
21
18
15

Answers

Answer:

Umm it has no photo so we can't see the table

Step-by-step explanation:

Umm it has no photo so we can't see the table

Answer: I had the same problem and someone else gave me the answer, the answer is B :>

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each graph to the equation of its line.

Answers

Answer:

If you're doing edmentum, maybe this will help. See Screenshot below. VVVVV

Step-by-step explanation:

The equation of the lines in the graphs given are:

Graph 1: y = -2x - 4

Graph 2: y = -x + 2

Graph 3: y = 4x - 4

Graph 4: y = x + 2

What is the Equation of a Line?

Equation of a line is given as, y = mx + b

m = slope = rise/runb = y-intercept.

Equation of the Line in Graph 1:

Slope = rise/run = -4/2 = -2

b = -4

Equation is: y = -2x - 4

Equation of the Line in Graph 2:

Slope = rise/run = -2/2 = -1

b = 2

Equation is: y = -x + 2

Equation of the Line in Graph 3:

Slope = rise/run = 4/1 = 4

b = -4

Equation is: y = 4x - 4

Equation of the Line in Graph 4:

Slope = rise/run = 2/2 = 1

b = 2

Equation is: y = x + 2

Learn more about equation of a line on:

https://brainly.com/question/13763238

#SPJ2

Please answer this correctly without making mistakes

Answers

Answer:

Its too low

Step-by-step explanation:

plz mark brainliestʕ•ᴥ•ʔ

There are 80 questions on a test. 1/4 of the answers are the letter A, 20% of the answers are letter B, 28 answers are the letter C, How many answers are the letter D?
18
28
20
16

Answers

Answer:

16

Step-by-step explanation:

1/4 is 20

20per is 16

20+16+28 is 64 minus 80 is 16

the linear equation y=1/2x+1 is represented by the graphed line. A second linear equation is represented by the data in the table. X(-2,0,2,4) Y(7,6,5,4) .In which square is the solution located​

Answers

Answer:

Correct Answer is D

Step-by-step explanation:

Answer:

Yeah it's "D"

Step-by-step explanation:

Have a Jocular Day

PLEASE ANSWER what are the slopes to these graphs ?

Answers

Answer:

13. 1/4x

14. -2/4x or -1/2x

15 1/3x or 2/6x

16. Zero

Step-by-step explanation:

13. goes up once and goes to the side 4 times

14. goes down twice and goes to the side 4 times

15. goes up one time and three to the side

16. zero slope, the line is horizontal

Answer:

13. 1/4

14. -1/2

15 1/3

16. Zero

Step-by-step explanation:

Explain how to calculate equivalent fractions.

Answers

Answer:

Hey there! Thanks for asking your question.

We can multiply the numerators and denominators by any number.

Either way, you will have the same equivalent fraction.

Let's do a practice problem:

[tex]\frac{1}{2} = ?[/tex]

We can multiply the numerator & denominator by 2.

We get the number [tex]\frac{2}{4}[/tex].

So, [tex]\frac{1}{2} = \frac{2}{4}[/tex].

Best of Luck!

What is the variable in Samuel is six inches taller than his brother Elijah.if Samuel is 48 inches tall,how tall is Elijah

Answers

Answer: Elijah would be 42 inches tall

Step-by-step explanation:

We all know that Samuel is 48 inches while Elijah is 6 inches shorter.

You subtract 6 from 48 to get 42.

Hopefully, this helped. :D

What is the value of the expression?
- 16+ 12
0-28
-4
4
O 28

Answers

-4 , when u add a negative to a positive u move up not down.

help me please......... ​

Answers

Answer:

1. true 2. true 3.true 4. false 5. false

Step-by-step explanation: 4/4-3/4 is 1/5. You multiply the top first (4-3=1) and the bottom isn't supposed to change. so the answer is 1/4

2n²-6n+5 for n=-3 pls help me

Answers

Answer:

41

Step-by-step explanation:

2n²-6n+5

2(-3)²-6(-3)+5

2(9)+18+5

18+18+5

36+5

41

Please help me find the line of the line showed

Answers

Answer:

[tex]m=\frac{1}{6}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (-5, -4)

Point (1, -3)

Step 2: Find slope m

Substitute:                   [tex]m=\frac{-3+4}{1+5}[/tex]Add:                             [tex]m=\frac{1}{6}[/tex]

plz help i will give u $10000
When the function f(x) is divided by 2x 1, the quotient is x2 93 3 and the
remainder is –9. Find the function f(x) and write the result in standard form.

Answers

Answer:

my cash app is Joy95H Suppose we wish to find the zeros of f(x) = x

3 + 4x

2 − 5x − 14. Setting f(x) = 0 results in the

polynomial equation x

3 + 4x

2 − 5x − 14 = 0. Despite all of the factoring techniques we learned1

in Intermediate Algebra, this equation foils2 us at every turn. If we graph f using the graphing

calculator, we get

The graph suggests that the function has three zeros, one of which is x = 2. It’s easy to show

that f(2) = 0, but the other two zeros seem to be less friendly. Even though we could use the

‘Zero’ command to find decimal approximations for these, we seek a method to find the remaining

zeros exactly. Based on our experience, if x = 2 is a zero, it seems that there should be a factor

of (x − 2) lurking around in the factorization of f(x). In other words, we should expect that

x

3 + 4x

2 − 5x − 14 = (x − 2) q(x), where q(x) is some other polynomial. How could we find such

a q(x), if it even exists? The answer comes from our old friend, polynomial division. Dividing

x

3 + 4x

2 − 5x − 14 by x − 2 gives

x

2 + 6x + 7

x−2 x

3 + 4x

2 − 5x − 14

x

3 −2x

2

6x

2 − 5x

6x

2 −12x)

7x − 14

− (7x −14)

0

As you may recall, this means x

3 + 4x

2 − 5x − 14 = (x − 2)

x

2 + 6x + 7

, so to find the zeros of f,

we now solve (x − 2)

x

2 + 6x + 7

= 0. We get x − 2 = 0 (which gives us our known zero, x = 2)

as well as x

2 + 6x + 7 = 0. The latter doesn’t factor nicely, so we apply the Quadratic Formula to

get x = −3 ±

2. The point of this section is to generalize the technique applied here. First up is

a friendly reminder of what we can expect when we divide polynomia

Step-by-step explanation:

the sum of three times x and 33

Answers

Answer:

3x+33

Step-by-step explanation:

This is if you are just looking for an expression.

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