the first 3 terms of the arithmetic sequence are given. find an expression t_ n in the terms of n and write the tenth term of each sequence​

The First 3 Terms Of The Arithmetic Sequence Are Given. Find An Expression T_ N In The Terms Of N And

Answers

Answer 1

Answer:

We get tₙ: [tex]\mathbf{t_n=an}[/tex]

10th term is [tex]t_{10}=10a[/tex]

Step-by-step explanation:

The given arithmetic sequence is: a,2a,3a

We need to find tₙ and tenth term

Finding tₙ

The formula used is: [tex]t_n=t1+(n-1)d[/tex]

We need to find d, the common difference

a₁ = a

a₂ = 2a

We can find common difference using the formula:

[tex]t_n=t_1+(n-1)d\\Put\:n=2\\t_2=t_1+(2-1)d\\2a=a+d\\d=2a-a\\d=a[/tex]

So, we get common difference d = a

Now, finding tₙ

[tex]t_n=t_1+(n-1)d\\t_n=a+(n-1)a\\t_n=a+an-a\\t_n=an[/tex]

So, we get tₙ: [tex]\mathbf{t_n=an}[/tex]

Now, finding 10th term

By putting n=10 in the equation [tex]t_n=an[/tex]

[tex]t_n=an\\Put\:n=10\\t_{10}=a(10)\\t_{10}=10a[/tex]

So, 10th term is 10a


Related Questions

A circle above has a radius of 6 cm. What is the area of the circle?

Use = 3.14.

Answers

Answer:

113.04

Step-by-step explanation:

formula for area is

pi times radius times radius

if the radius is 6,

do 6 times 6=36

36 times 3.14=113.04

113.04 will be ur answer

The Blackburn family has a square field where they keep their cattle. The area of the field is 40,000 ft2, and Mr. Blackburn wants to put a fence diagonally through the field. What should the length of the fence be? *


282.8 feet
4,000 feet
782.6 feet
8,000 feet

Answers

Answer:

Length of the fence will be = 282.84 feet

Step-by-step explanation:

The Blackburn family has a square field to keep their cattle. Area of the field is $40000 square feet.
Then one side of the square field will be = √Area = √40000 = 200 feet
Since diagonal of a square is = √2(side)² = side√2 = 200√2 = 200×1.41 = 282.84 feet.

Therefore length of the fence will be = 282.84 ft.

How to make a simplified expression for 4(y + 3) - 5

Answers

Answer:

4y + 7

Step-by-step explanation:

Simplify. Use the distribution method, and follow PEMDAS.

PEMDAS is the order of operation. It stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

Distribute 4 to all terms within the parenthesis. In this case, you are multiplying 4 to all the terms:

4(y + 3) = (4 * y) + (4 * 3) = 4y + 12

Next, combine like terms (terms with the same amount of variables);

4y + 12 - 5

4y + (12 - 5)

4y + 7

4y + 7 is your simplified expression.

~

Find the length of BC on triangle ABC. ​

Answers

the length of bc is 8

The weights in pounds of 6 members of a basketball team are 125, 136, 150, 119,
and 143. Find the mean and the median *

Answers

Answer:

Mean:(137.2)

Median:(139.5)

Step-by-step explanation:

Mean = (125+136+150+119+143) divide by six(6)

= 823/6 = approx 137.2

Median = for the median, you will arrange the numbers in other. from smaller to the bigger number.

119,125,136,143,150, 150. so 136 & 143 is the middle number.

so you will add the middle number and divide by 2.

that is 136+143/2 = 139.5.

On Monday, the high was 60 degrees Fahrenheit in the Capitol. On Tuesday, the high was 18% more. What was the temperature on Tuesday?

Answers

Answer: 78 degrees

Step-by-step explanation:

What is the key slope word in the problem?
A car rental company charges a $50 deposit and $25 per day.

Answers

Answer:

The equation will be y=25x+50

Step-by-step explanation:

This is because 50 is only being charged once and is the constant.

They are charging $25 per day thus that is the slope.

If y=1/2*x+3, which ordered pair is one of the solutions for the equation and the coordinates for one of the points on
the graph

Answers

Step-by-step explanation:

D (-2,2)

:) good day

good day

enter a negative number that is greater than -10

Answers

Answer:

-9

Step-by-step explanation:

Can I have brainliest?

Also can you please thank me, it'll be gratefully appreciative.

:)

X/-5=1.2

Solve the equation for the value of the equation for the value of the variable show all work please and thanks :):)

Answers

well u can transfer the -5 in denominator to the right hand side

so x=1.2*(-5)

x=-6.0

Evaluate the given expression for x= 13.
2x + 3
The answer is

Answers

Answer:

no

Step-by-step explanation:

no

What is the slope intercept form of the line that
has a slope of 4 and passes through the point (3. -
10)?

Answers

Y= 4(x-3) +10 so y=4x-2

Answer:

y=4x-22

Step-by-step explanation:

slope intercept form: y=mx+b

STEPS:

y-y1=m (x-x1)  <---- The formula to solve ity--10=4(x-3)    y+10=4x-12   -10       -10y=4x-22 <---- Final Answer

Hope this helps!

Solve for 3.
Enter the solutions from least to greatest.
2x2 - 5 = 13
lesser x =
greater 2 =

Answers

Answer:

lesser: x = -3

greater: x = 3

Step-by-step explanation:

[tex]2x^{2} =18\\x^{2} =9\\x=-3, x=3[/tex]

b. Mills works as a construction worker. He makes a salary of 54,200 a year. After
this year his boss decided to give him a 3.5% raise. What is his new salary?

Answers

Answer:

$56,097

Step-by-step explanation:

First, we have to figure out how much his raise was, so we can convert 3.5% directly to a decimal:

3.5% = 0.035

Then we find

3.5% of 54,200 = 0.035 x 54,200 = 1,897

1,897 + 54,200 = 56,097

So, Mills new salary is $56,097

hope this helps:)

please help me thank you if you can help

Answers

Answer:

24 for the 2 batches, 84 for the 7 batches, 72 for the white sugar

x = 6y – 14
-X + 9y = 17

Answers

Answer:

(x, y)=(-8,1) this is substantial method

what is the slope? Pls help

Answers

Answer:

-1/7

Step-by-step explanation:

What is the range of function g?

Answers

Answer:

c

Step-by-step explanation:

but if C is incorrect i believe your second choice should be D

Answers

A. 10
B. 5
D. 15
C. 20

Answers

Answer:

D: 15

Step-by-step explanation:

Ok, by looking at the first equation, you know that one triangle equals 10. By looking at the second one, you see that two circles equal 10, since 20- triangle(10) equals 10. This means a circle has to equal 5. looking at the third one, the answer is 13, and a circle is 5, so 13-5=8. Two squares equal 8. the last one shows one triangle, one circle, and a half square. From the third one, you know that one square equals 4, so a half square equals two. I do not know why this logic doesn't match with the answers, since 10(triangle) plus 5(circle) and 2(half square) is 17, but in terms of what makes sense and just matching it with the answers provided, I say go with the third option.  

12+90+x=180 I need help fast

Answers

Answer:

78

Step-by-step explanation:

102+x=180

x=180-102

x=78

any easy way to remember the 8 and or 7 ×tables?​

Answers

Answer:

nope

Step-by-step explanation:

sorry about not knowing how to

Answer:

08

16

24

32

40

48

56

64

72

80

Step-by-step explanation:

From 1-10 You can see the numbers going from 0-8 on the left side except you repeat the number 4 twice then proceed. Then on the right side you do it backwards but instead you use the 2 times tables and you’re going to want to work your way from bottom to top and then when you reach to 0 which is the number 10 you repeat the 2 times tables again.

An angle θ on the unit circle has a sine of 14. What is the value of cosθ?

Answers

Given:

An angle θ on the unit circle has a sine of [tex]\dfrac{1}{4}[/tex].

To find:

The value of cosθ.

Solution:

We have,

[tex]\sin \theta=\dfrac{1}{4}[/tex]

Since sinθ is positive, therefore, θ lies in first or second quadrant.

We know that,

[tex]\sin^2 \theta +\cos^2 \theta =1[/tex]

[tex](\dfrac{1}{4})^2+\cos^2 \theta =1[/tex]

[tex]\dfrac{1}{16}+\cos^2 \theta =1[/tex]

[tex]\cos^2 \theta =1-\dfrac{1}{16}[/tex]

Taking square root on both sides.

[tex]\cos \theta =\pm \sqrt{\dfrac{16-1}{16}}[/tex]

[tex]\cos \theta =\pm \dfrac{\sqrt{15}}{4}[/tex]

Therefore, the value of cosθ is either [tex]\dfrac{\sqrt{15}}{4}[/tex] or [tex]-\dfrac{\sqrt{15}}{4}[/tex].

Plz Answer 25 points
The table shows the height of water in a pool as it is being filled.

The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool?

1. The height of the water increases 2 inches per minute.
2. The height of the water decreases 2 inches per minute.
3. The height of the water was 2 inches before any water was added.
4. The height of the water will be 2 inches when the pool is filled.

Just say the number

Answers

Answer:

The answer is 1.

Step-by-step explanation:

None.

The surface area of the pyramid is

square inches.
fill in the blank

Answers

Answer:

9360 square inches

Step-by-step explanation:

The graph shows a proportional relationship between the cost of grapes, in dollars, and the number of pounds of grapes.

Answers

Answer:

where is the picture

Step-by-step explanation:

Answer:

where's the picture?

Step-by-step explanation:

Simon says that to find the area of a trapezoid, you can multiply the height by the top base and the height by the bottom base. Then add the two products together and divide the sum by 2. Is Simon correct? Complete the explanation.

Answers

Answer:

Yes, Simon is correct.

Step-by-step explanation:

A trapezoid refers to a quadrilateral that is convex in shape; as such it has no equal sides and no parallel sides.

Let the height of a trapezoid be h.

Let the top base of a trapezoid be b1.

Let the bottom base of a trapezoid be b2.

[tex] Area \; of \; trapezoid = \frac {1}{2} * (Sum \; of \; nonparallel \; sides) * height [/tex]

Therefore, [tex] Area \; of \; trapezoid = \frac {1}{2} * (b_{1} + b_{2}) * h [/tex]

[tex] Area \; of \; trapezoid = \frac {1}{2} * (b_{1}h + b_{2}h) [/tex]

[tex] Area \; of \; trapezoid = \frac {b_{1}h + b_{2}h}{2} [/tex]

Hence, to find the area of a trapezoid, you will multiply the height by the top base and the height by the bottom base. Then you add the two products together and divide the sum by 2.

If 4x+3x-2(x+5)=-9 then x=?

Answers

Answer:

X=1/5

Step-by-step explanation:

7×-2×-10=-9

5×=-9 +10

5×/5=1/5

×=1/5

Which equation represents the standard form for linear equations?
A y= 5x – 2
B. 3x – 5 = 2y
C. 1/2x+ 2y = 7
D. 5x– 4y = 20

Answers

Answer:

Ax + By = C the answer is C 1/2x+2y=7

Step-by-step explanation:

Which is the equation of a line that has a slope of Negative two-thirds and passes through point (–3, –1)?

Answers

Answer:

Y=2/3x+1

Step-by-step explanation:

PLEASE HELP ME I AM SO CONFUSED!!

Answers

A. Isosceles, Not right



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