The 4th and the last terms of an A.P. are 11 and 89 respectively. If there are 30 terms in the A.P., find the A.P. and its 23rd term.​

Answers

Answer 1

[tex]\underline{\underline{\large\bf{Given:-}}}[/tex]

[tex]\red{\leadsto}\:[/tex][tex]\textsf{} [/tex][tex]\sf Number \: of \:terms \: in \: A.P,n = 30[/tex]

[tex]\red{\leadsto}\:[/tex][tex]\textsf{} [/tex][tex]\sf Fourth \: term ,a_4 = 11 [/tex]

[tex]\red{\leadsto}\:[/tex][tex]\textsf{} [/tex][tex]\sf last\:term, a_{30} = 89 [/tex]

[tex]\underline{\underline{\large\bf{To Find:-}}}[/tex]

[tex]\orange{\leadsto}\:[/tex][tex]\textsf{ } [/tex][tex]\sf The \: A.P. [/tex]

[tex]\orange{\leadsto}\:[/tex][tex]\textsf{ } [/tex][tex]\sf 23rd\: term, a_{23} [/tex]

[tex]\\[/tex]

[tex]\underline{\underline{\large\bf{Solution:-}}}\\[/tex]

The nth term of A.P is determined by the formula-

[tex]\green{ \underline { \boxed{ \sf{a_n = a+(n-1)d}}}}[/tex]

where

[tex]\sf a = first \:term[/tex][tex]\sf a_n = nth \: term[/tex][tex]\sf n = number \:of \:terms [/tex][tex]\sf d = common \: difference [/tex]

Since ,

[tex]\sf a_4 = 11 [/tex]

[tex]\longrightarrow[/tex] [tex]\sf a+(4-1) d= 11 [/tex]

[tex]\longrightarrow[/tex] [tex]\sf a+3d= 11\_\_\_(1) [/tex]

[tex]\sf a_{30}= 89 [/tex]

[tex]\longrightarrow[/tex] [tex]\sf a+(30-1)d=89[/tex]

[tex]\longrightarrow[/tex][tex]\sf a+29d= 89\_\_\_(2)[/tex]

Subtracting equation (1) from equation(2)

[tex]\begin{gathered}\\\implies\quad \sf a+29d-(a+3d) = 89-11 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a+29d-a-3d = 78 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a-a+29d-3d = 78 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf 26d = 78 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf d = \frac{78}{26} \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf d = 3 \\\end{gathered} [/tex]

Putting the value of d in equation (1) -

[tex]\begin{gathered}\\\implies\quad \sf a+3(3) = 11 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a = 11-9 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a = 2 \\\end{gathered} [/tex]

First term of A.P, a = 2

Second term of A.P.,[tex]\sf a_2= 2+(2-1)\times 3[/tex]

[tex]\quad\quad\quad\sf =2+3[/tex]

[tex]\quad\quad\quad\sf =5 [/tex]

Third term of A.P.,[tex]\sf a_3= 2+(3-1)\times 3[/tex]

[tex]\quad\quad\quad\sf =2+6[/tex]

[tex]\quad\quad\quad\sf =8 [/tex]

[tex]\longrightarrow[/tex]Thus , The A.P is 2,5,8,. . . . . .

Now,

[tex]\begin{gathered}\\\implies\quad \sf a_n = a+(n-1)d \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a_{23 }= 2+(23-1)\times 3 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a_{23} = 2+22 \times 3 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a_{23} = 2+66 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf a_{23} = 68 \\\end{gathered} [/tex]

[tex]\longrightarrow[/tex]Thus , 23rd term is 68.


Related Questions

Pleaseee helppp meee question 2 !!!

Answers

just plot it in the graph
start by taking a coordinate in the xy table like 1,3 and find 1 on the x axis and 3 on the y and find where they cross and draw a point

7.
Meredith spent $367.80 on tulip mand daffodil bulbs for her
flower bed. A bag of tulip bulbs Meredith spent $367.80 on tulip and daffodil bulbs for her flower bed. A bag of tulip bulbs cost $7.95 and daffodil bulbs cost $6.80 per bag. If she bought three times as many tulips as daffodils, how many bags did she buy of each kind?
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The answer is 365 don’t listen to me

Find the value of xxx in the triangle shown below.

Answers

Answer:

Can I get image of it?

Step-by-step explanation:

Answer:

Image?

Step-by-step explanation:

HELP!!! NEED RATIO! A TON OF POINTS!

Answers

The length of CD IS 3 and AC IS 8 hope this helps

Answer:

yes

Step-by-step explanation:

Triangle XYZ has vertices X(1, 3), Y(0, 0), and Z(–1, 2). The image of triangle XYZ after a rotation has vertices
X'(–3, 1), Y'(0, 0), and Z'(–2, –1). Which rule describes the transformation?

R0, 90°
R0, 180°
R0, 270°
R0, 360°

Answers

Answer:

ur answer is.. 90 degree

Step-by-step explanation:

Triangle ABC was transformed using the rule (x, y) -> (-y, x). The vertices of the triangle are shown.

Which best describes the transformation?

would be a R0, 90 degree  

i jst took the quiz....

Answer:

90 degrees

Step-by-step explanation:

It takes Jamil 40 minutes to drive to work, plus or minus 8 minutes depending on traffic. Which of the following equations could be solved to find the shortest or longest times she might drive?

Answers

Answer:

addition

Step-by-step explanation:

add 40+8 and you get 48 :P

Find the product of-10/5 x (-15/5)

Answers

Answer:

6

Step-by-step explanation:use math- way it will help you in future

Answer:

6

Step-by-step explanation:

Equation: [tex]-\frac{10}{5}\cdot -\frac{15}{5}[/tex]

1). Apply [tex]-a(-b)-ab[/tex]: [tex]-\frac{10}{5}(-\frac{15}{5}=\frac{10}{5}\cdot \frac{15}{5}[/tex]

2). [tex]\frac{10}{5}[/tex] simplfies to 2, so [tex]2\cdot \frac{15}{5}[/tex]

3). [tex]2\cdot 3[/tex]

15. Find the value of x.
(7x-1)
(6x - 1)
X =

Answers

Answer:

the answer is -1

Step-by-step explanation:

Answer: x = 0

Step-by-step explanation: Firstly, set them equal to each other.

7x - 1 = 6x - 1

Now, subtract 6x from both sides:

x - 1 = -1

Add 1 to both sides:

x = 0

And if you need to know what type of function it is, it is an infinite function because if you plug in 0:

7(0) - 1 = 6(0) - 1

You get:

-1 = -1

If both sides are the same, it is an infinite function.

Hope this helps!

solve for x. 36x+2=110. show work

Answers

Answer:

Answer to x is 3. so it would be x = 3

Answer:

x=3

Step-by-step explanation:

36x+2-2=110-2

36x=108

36x/36=108/36

x=3

what is the value of the 2 in 0.812

Answers

Answer:

the two is in the thousandths place

Step-by-step explanation:

the eight is in the tenths, and the one is in the hundredths

Answer:

.8 tenths

.01 hundredths

.002 thousandths

so the value of 2 would be 2 thousandths or .002 thousandths

27/x = 9/6 fraction on get more math

Answers

Answer:

18

Step-by-step explanation:

Need help, will mark brainliest plus 50 points.

Lia gets paid $450 a week plus a
5% commission on her sales. She
hopes to earn at least $600
dollars each week.
a. Write an inequality to
represent the verbal
description.
b. How much does Lia
need in sales to make
her goal?

Answers

Answer:

Step-by-step explanation:

To write the inequality, we need to first caculate the amount of money that Lia would ACTUALLY earn each week and compare that to her goal of $600.

We cannot actually get the amount of money that Lia would get because we don't know her sales so we will represent the sales with a X.

450+ X(5%).  -This the amount of money she would egt from her sales. We need to also figure out 5% of 450 to solve the next part of the equation. That is $22.5. 600-450=150/22.5= 6.6666- which is about 7 sales.

i really do not know the answer

Answers

Answer: the answer is D which is really the only answer higher then $36.99

Step-by-step explanation:

Answer: d. 38.47

Step-by-step explanation:

Carlos makes baskets with bags of coffee or boxes of tea. He has 72 bags of coffee and 56 boxes of tea. He wants to put an equal number of bags of coffee and boxes of tea in each basket. Each basket contains only coffee or tea. A. What is the largest number of bags of coffee or boxes of tea that he can put in each basket?

Answers

Answer:

1

Step-by-step explanation:

1

Mr. Townsend bought five hot dogs for his family from the concession stand. Each hot dog cost
$
1.75
. How much change will he get back if he gives the cashier
$
10
? Show your work, including labeling your answer with the appropriate units of measure.

Answers

Answer:

1.25

Step-by-step explanation:

so you multiply 1.75 by 5 which is 8.25. You subract 10 by 8.25

alex is working to simplify 5·(-8)·2


A. what is the product?

B. suppose Alex found the opposite of the correct product. describe an error he could have made that resulted in that product.

please answer quickly!!!!!!!!!!!!

Answers

Answer:

A. 5*(-8)*2=-80

B. Forgot about the signs

Step-by-step explanation:

Product of Signed Integers

The product of two integers with like (same) signs is positive. The product of two integers with different signs is negative.

A.

Alex is simplifying the product 5*(-8)*2. It can be done in any order, for example, let's multiply 5*(-8) first.

The numbers have different signs, so the product is negative and 8*5 =40, thus:  5*(-8)=-40.

Now we finish the operation multiplying (-40)*2. They have different signs, thus the result is negative and (-40)*2=-80, thus:

5*(-8)*2=-80

B.

If Alex found the opposite of the correct product, that is, 80 is more likely to have been the result of forgetting about the signs. He probably just multiplied the numbers regardless of their signs.

What is 1.2 simplified

Answers

Answer:

it is 1 2/10 but simplified to 1 1/5

Step-by-step explanation:

Jackie is diving 25.65 feet below sea level and then dives down another 16.5 feet. Then he rose 12.45 feet. What is Jackie’s new depth?

Answers

Answer:

-29.7

Step-by-step explanation:

Assuming sea level is at 0, you would first subtract 25.65 from 0 to indicate diving 25.65 feet BELOW 0. Then, you subtract 16.5 from that. Then, add 12.45 to that number to get the answer after the diver rose 12.45 feet.

0-25.65= -25.65

-25.65-16.5= -42.15

-42.15+ 12.45= -29.7

OR 29.7 feet below sea level.

someone answer this??

Answers

Answer:

corresponding angle

Step-by-step explanation:

In a library 20% of the books are fiction (a) what percentage are non fiction?(b) if there are 6000 books in the library. how many are fiction and how many are non fiction​

Answers

Answer:

A) 80%

B) Non-Fiction = 4,800 books Fiction = 1,200 books

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answers:

a) 80% nonfiction

b) 1200 fiction, 4800 nonfiction

=========================================

Explanation:

part (a)

We only have two choices: fiction or nonfiction

If 20% are fiction, then 100% - 20% = 80% are nonfiction.

The two percentages 20% and 80% add to 100% to represent all the books.

---------------------

part (b)

20% = 20/100 = 0.20

20% of 6000 = 0.20*6000 = 1200

we have 1200 fiction books

6000-1200 = 4800

and we have 4800 nonfiction books

Note how

80% of 6000 = 0.80*6000 = 4800

which helps confirm part (a)

What is the Value of
3.1 + (-4) - (-0.7)
i mostly want to just check my answer

Answers

3.1+(-4)-(-0.7)
3.1-4+0.6
-0.2

A rectangular lawn is 8 meters wide and 18 meters long. What is the perimeter?

Answers

Answer:

8x2=16 18x2=36 16+36=52

Step-by-step explanation:

a rectangle has four sides so two sides have to be 8 and the other two have to be 18

Answer:

52

Step-by-step explanation:

1. 8*2=16

2) 18*2=36

3)36+16=52

You ride the train to an after-school job every weekday. The ticket for the trip from school to work costs $3. The ticket for the trip from work back home costs d dollars. How much do you spend on train tickets each day? How much do you spend in a 5-day week?

Answers

Answer:

each day= 3+d

each 5-day week= 15+5d

Step-by-step explanation:

Between which two consecutive whole numbers does \sqrt{3} 3 ​ lie? Fill out the sentence below to justify your answer and use your mouse to drag \sqrt{3} 3 ​ to an approximately correct location on the number line. Between which two consecutive whole numbers does \sqrt{3} 3 ​ lie? Fill out the sentence below to justify your answer and use your mouse to drag \sqrt{3} 3 ​ to an approximately correct location on the number line.

Answers

Answer:

It lies between 5 and 6

Step-by-step explanation:

Two consecutive numbers are numbers that come after each other:

x , x + 1 are consecutive numbers.

3 \sqrt{3} = 3√3 = 5.19615242271

Therefore, from the above calculation, we can see that square root of 3 is a number that is between consecutive numbers 5 and 6

Answer:

It lays Between 2 and 3

In one month, the median home price in the west fell from $203,400 to $192,300. Find the percent decrease

Answers

around 5.4572271...% decrease
(i’m not sure what to round it to)

subtract 192,300 from 203,400 to find the amount of change
(= 11,100)

then divide that amount from the original price (203,400)

then multiply that number by 100 to get a percent

finally round to a reasonable percent
203,400-192,300=11,100
11,100/203400= 5.46%
It decreased by 5.46%

What is the equation of this line?
y= 4/5x-3
y=5/4x-3
y=4/5x+3
y=-4/5x-3

Answers

Answer:

the answer is y=4/5x-3

The equation of the line shown in the graph would be, [tex]y = \dfrac{4}{5} x - 3[/tex]

Hence, option 1 is true.

Given that;

Two points on the line are (5, 1) and (0, -3).

Used the concpet of the equation of the line,

The equation of a line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, [tex]m = \dfrac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]

Now,

Since, The equation of line passes through the points (5, 1) and (0, -3)..

So, We need to find the slope of the line.

Hence, the slope of the line is,

[tex]m = \dfrac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]

[tex]m = \dfrac{(- 3 - 1)}{(0 - 5)}[/tex]

[tex]m = \dfrac{(- 4)}{( - 5)}[/tex]

[tex]m = \dfrac{(4)}{( 5)}[/tex]

Thus, The equation of the line with slope 4/5 is,

[tex]y - 1 = \dfrac{4}{5} (x - 5)[/tex]

[tex]y - 1 = \dfrac{4}{5} x - 4[/tex]

[tex]y = \dfrac{4}{5} x - 4 + 1[/tex]

[tex]y = \dfrac{4}{5} x - 3[/tex]

Therefore, The equation of the line will be;

1) [tex]y = \dfrac{4}{5} x - 3[/tex]

So, option 1 is true.

To learn more about the equation of line visit:

https://brainly.com/question/18831322

#SPJ6

Convert to a decimal. 164%

Answers

Answer:

1.64

Step-by-step explanation:

Step-by-step explanation:

to remove percentage divide value with 100

164/100

answer in fraction

41/25

answer in decimal

1.64

Please help! Select the graph of the solution. 2x - 1 > 5

Answers

Answer:

See photo below

Step-by-step explanation:

First, start solving it. Add 1 to each side, so it now looks like this: 2x > 6Divide each side by 2 to cancel out the 2 next to x. It should now look like this: x > 3Now, look at your options and pick the graph that fits the solved equation. The last option matches the solved equation exactly, so that's the answer.

I hope this helps!

x>3
add 1 to both sides than divide by 2 and you get x is greater than 3
your graph would be open circle on the 3 going right

1+1=?
5
2
4
7
this question is really hard and confusing

Answers

Answer:

I think it is 2

Step-by-step explanation:

I hope this is right! Please Rate Brainiest!

Answer:

its obv 478

Step-by-step explanation:

1+1=2 divoided by 400=294-478

King Kyle orders the construction of his future mausoleum (a fancy tomb) so that people never forget his awesomeness. His architect draws a floor plan depicting the mausoleum as a rectangle measuring 35\text{ m}35 m35, start text, space, m, end text by 40\text{ m}40 m40, start text, space, m, end text. Move points to redraw the architect's floor plan on the grid below.

Answers

Answer:

see attached image

Step-by-step explanation:

The mausoleum's plan measures 35 (width) by 40 (height) meters. Each square represents 2.5 m. When you redraw the tomb on the grid, it should measure 14 (width) by 16 (height) squares.

Answer:

Step-by-step explanation:

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