The 17th term of an Arithmetic sequence is 51. If the commons difference is 7, what is the first term ?

Answers

Answer 1

Answer:

The first term is:

[tex]a_1=-61[/tex]

Step-by-step explanation:

The arithmetic sequence is defined by

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

where

[tex]a_1[/tex] is the first term

[tex]d[/tex] is the common difference

as

the 17th term of an arithmetic sequence is 51.

i.e. [tex]a_{17}=51[/tex]

so

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

[tex]a_{17}=a_1+\left(17-1\right)d[/tex]        

[tex]51=a_1+\left(17-1\right)7[/tex]         ∵ [tex]n = 17[/tex], [tex]a_{17}=51[/tex] , [tex]d=7[/tex]

[tex]a_1+112=51[/tex]                   ∵ [tex]\left(17-1\right)\cdot \:\:7=112[/tex]

[tex]a_1=-61[/tex]

Therefore, the first term is:

[tex]a_1=-61[/tex]

Related Questions

Of the following, which is the solution to 2x2 + 3x = −5?

Answers

Answer:

Step-by-step explanation:

Nothing to choose from??/

But 2x^2+3x=-5 is

- 3± i√31 / 4

Answer:

[tex]\frac{-3+-i\sqrt{31} }{4}[/tex]

ye

What is the slope in the equation y=3/4x

What is the y-intercept also?

Answers

Answer:

slope = 3/4

y- intercept : (0,0)

Step-by-step explanation:

Sixth grade Y.14 Factor using th
Factor 10y + 20z.

Answers

Answer:

17zy

Step-by-step explanation:

big brain

Answer:

y+z=30

Step-by-step explanation:

y=10 z=20

y+z=30

In a survey of 2,800 people who owned a certain type of​ car, 1,400 said they would buy that type of car again. What percent of the people surveyed were satisfied with the​ car?

Answers

Answer:

50% of people would buy the car again.

Step-by-step explanation:

2800 divided by 2 is 1400.

The percent of the people surveyed were satisfied with the​ car is 50%.

Given that,

In a survey of 2,800 people who owned a certain type of​ car, 1,400 said they would buy that type of car again.

Based on the above information, the calculation is as follows:

[tex]= 1400 \div 2800[/tex]

= 50%

Learn more: https://brainly.com/question/10309631?referrer=searchResults

A deal is a deal, so here is a good one, let's see who gets it right. I had $10.00. My mom gives me $30.00, My dad gave me $30.00. My aunt and uncle give $100.00. I had another $10.00. How much money did I have?

Answers

Answer:

$180 in total!

Step-by-step explanation:

10 + 30 + 30 + 100 + 10 = 180

the uncle and aunt gave their money together, it didn't specify that they each gave 100

Answer:

The total amount of money i have is $180.

Step-by-step explanation:

Given information:

The money i have = $10

Mom gives = $30

Dad gives = $30

Aunt and uncle gives = $100

Now i had another $10

The total amount of money (x) i have is the sum of all money i receive.

x = 10+30+30+100+10

x = 180

Hence , the total amount of money i have is $180.

For more information visit:

https://brainly.com/question/4356723?referrer=searchResults

3(6d - 24) = 6(12 + 3d)
pls solve i need

Answers

3D = 32 or D = (10 2/3)

Step-by-step explanation:

We want to make D only one side so we subtract 3D from the left

Then we slowly make the equation smaller and smaller by adding 24 to each side, multiplying the numbers, then finally getting our answers.

Answer:

No solutions

Step-by-step explanation:

Distribute the 3 to the first set of parentheses:

3(6d - 24) = 6(12 + 3d)

18d - 72 = 6(12 + 3d)

Distribute the 6 to the other set of parentheses:

18d - 72 = 72 + 18d

Subtract 18d from both sides:

-72 = 72

-72 [tex]\neq[/tex] 72

Since -72 and 72 are not equal, there are no solutions

PLEASE HELP!!
You need to factor by grouping.
Please explain the steps!

Answers

Answer:

3(k-4)(7k^2+5)

Step-by-step explanation:

1) Factor out GCF

3(7k^3-28k^2+5k-20)

2)Split into two

3) Factor

3*7k^2(k-4)+5(k-4)

3(k-4)(7k^2+5)

2-\dfrac12n=3n+162− 2 1 ​ n=3n+16

Answers

Answer:

2-\dfrac12n=3n+162− 2 1 ​ n=3n+162-\dfrac12n=3n+162− 2 1 ​ n=3n+162-\dfrac12n=3n+162− 2 1 ​ n=3n+162-\dfrac12n=3n+162− 2 1 ​ n=3n+162-\dfrac12n=3n+162− 2 1 ​ n=3n+162-\dfrac12n=3n+162− 2 1 ​ n=3n+162-\dfrac12n=3n+162− 2 1 ​ n=3n+162-\dfrac12n=3n+162− 2 1 ​ n=3n+16

Step-by-step explanation:

May I have brainliest please? :)

Please help, please write a proof to prove the “prove” section

Answers

it’s the triangle 1244

Tao wants to check that the expression 3(4x – 6) simplifies to 12x – 18. What is the value when 2 is substituted for x into both expressions? The value of each expression is 2. The value of each expression is 6. The value of one expression is 2, and the value of the other expression is 6. The value of one expression is 6, and the value of the other expression is –6.

Answers

Answer:

The value of each expression is 6.

Step-by-step explanation:

3 * 4 = 12 and 3 * 6 = 18

So 3(4x - 6) = 12x - 18

12(2) - 18 = 24 - 18 = 6

Answer:

the value of each expression is 6

Step-by-step explanation:

edge 2020

15% off of $60, then subtracting 10% from that cost, is equal to

Answers

Answer:

8.1 i think

Step-by-step explanation:

Inside an auditorium, 1 out of 5 people wear hats, and 4 out of 5 people do not wear hats. Based on this information, predict how many wear hats if there are 215 people.

Answers

Answer:

43

Step-by-step explanation:

Haley spent 1/2 hour playing on her cell phone that use 1/9 of her battery how long does she have to play on her phone to use the entire battery?

Answers

Answer:

4 1/2 hours.

Step-by-step explanation:

If 1/2 an hour only used up 1/9 of her battery, 9, 1/2 would give us 9/2, which if you simplified it gets you 8 1/2 hours. Hope this helps! Have a great day!

say hi and i will mark brainllyist or whatever

Answers

Answer:

hi hows your day

Step-by-step

Find k such that the roots of the quadratic are real, rational, and equal: 9x^2+kx+1=0

Answers

Answer:

Step-by-step explanation:

9x^2+kx+1=0

k= -9x-1/x

Which of the following points would be on the graph of the equation y=−4x+6?(−4, −10)(−4, 22)(1, −10)(1, −2)

Answers

Answer:

Only the point (-4, 22)  is ON THE GRAPH of the equation. Please also check the attached graph.

Step-by-step explanation:

Given the equation

[tex]y=-4x+6[/tex]

Let us substitute all the given points to check which points satisfy the equation.

Substitute (-4, -10) in the equation

[tex]y=-4x+6[/tex]

[tex]-10=-4(-4)+6[/tex]

[tex]-10=16+6[/tex]

[tex]-10=22[/tex]

As the R.H.S ≠ L.H.S, hence (-4, -10) does not satisfy the equation.

Hence, (-4, -10) is NOT ON THE GRAPH of the equation

Substitute (-4, 22) in the equation

[tex]y=-4x+6[/tex]

[tex]22 = -4(-4)+6[/tex]

[tex]22 = 16+6[/tex]

[tex]22 = 22[/tex]

As the R.H.S = L.H.S, hence (-4, 22) satisfies the equation.

Hence, (-4, 22)  is ON THE GRAPH of the equation. Please also check the attached graph.

Substitute (1, -10) in the equation

[tex]y=-4x+6[/tex]

[tex]-10=-4(1)+6[/tex]

[tex]-10=-4+6[/tex]

[tex]-10=2[/tex]

As the R.H.S ≠ L.H.S, hence (1, -10) does not satisfy the equation.

Hence, (1, -10) is NOT ON THE GRAPH of the equation

Substitute (1, -2) in the equation

[tex]y=-4x+6[/tex]

-2 = -4(1)+6

-2 = -4 + 6

-2 = 2

As the R.H.S ≠ L.H.S, hence (1, -2) does not satisfy the equation.

Hence, (1, -2) is NOT ON THE GRAPH of the equation

Therefore, from the above analysis, we conclude that only the point (-4, 22)  is ON THE GRAPH of the equation. Please also check the attached graph.

Question 1
Find an expression equivalent to 8(2x+1)(x-2)(x+3)

Answers

Answer:

18x + 13

Step-by-step explanation:

just add like terms after multiplying 2x + 1 by 8

16x + 8

x - 2

x + 3

18x + 13

What is the 4th equivalent fraction to 1/8

Answers

Answer:

2/16

Step-by-step explanation:

this is the 4th equivalent fraction to 1/8

(-3, 8) is a solution to the following system of equations: 4x + 3y = 12 5x + 2y = 1 True False

Answers

Answer: True

Step-by-step explanation:

question 4 pleeeeease help

Answers

It should be B because it is the only one with a negative sign. The first one is not a slope problem.

Aanya got 5 marks in Science test. Her friend Sneha got 'x' marks more than Aanya. How many marks did they get altogether?

Pls Answer FAST

Answers

10 + x i hoped this helped

Understanding Elevation
Death Valley, Califomia, has an elevation of -282 feet What does this mean?
It is 282 feet above sea level
It is 282 feet below sea level.
It is - 282 feet above sea level
Itis - 282 feet below sea level

Answers

Answer:

Step-by-step explanation:

if it has a negative elevation of 282 feet than its below sea level by 282 feet if its 282 feet above with no negative than its 282 feet above sea level i hope this helped

Answer:

hi the answer is b)It is 282 feet below sea level.\

have a nice day!

Step-by-step explanation:

mark me brainliest?

Exercise 1: Which of the following is not an equation
(1) 2x + 3 = 10
(2) 3+2 = 5
(3) 3(2x + 1)
(4) 1+ 4 = 10

Answers

It is number 4.........

Answer:

(3) 3(2x +1 )

Step-by-step explanation:

For (1), (2), and (4), all of them give an answer while (3) does not which means that (3) is not an equation.

the douglas family visits sealand and is charged $72.00 for 2 adults and 3 child tickets. the williams family also visited sealand and was charged $78.00 for 1 adult and 5 child tickets. how much would it cost the lopez family to go to sealand if they have 3 adults and 4 children

Answers

SIMULTANEOUS EQUATIONS
2a + 3c = 72
1a + 5c = 78 you need to get one of them the same so do 1a +5c=78 x2 =
2a + 10c = 156 , then 2a + 10c = 156 subtract 2a +3c= 72 which is 7c = 84 divide by 7 each side so c = 12 so a child ticket is £12 then so the same for the adults so 2a +3c= 72 x 5 = 10a + 15c =360 then do 1a + 5c = 78 x3 = 3a + 15c= 234 then 10a + 15c =360 subtract 3a + 15 c= 234 = 7a = 126 then divide by 7 each side so a = 18 so an adults ticket is £18
Then do 18 + 18 + 18 + 12 + 12 + 12 + 12 = 102 so it would cost the Lopez family £102 to go to sea-land

hope this makes sense .

Is the sequence arithmetic? If yes, determine the common difference. *
(1 Point)
-14-9, -4, 1, 6, ...
O no, it does not increase or decrease the exact same amount
O yes, d = 5
O yes, d = -5

Answers

Answer:

Option 2: Yes, d= 5 is the correct answer

Step-by-step explanation:

An arithmetic sequence is a sequence where the common difference between the consecutive terms is same.

Given arithmetic sequence is:

-14, -9, -4, 1, 6

To check if it is an arithmetic sequence, we have to find the common difference d

[tex]a_1 = -14\\a_2 = -9\\a_3 = -4\\a_4 = 1[/tex]

Now,

[tex]d = a_2-a_1 = -9-(-14) = -9+14 = 5\\d = a_3 - a_2=-4-(-9) = -4+9 = 5\\d = a_4-a_3 = 1-(-4) = 1+4 = 5[/tex]

As the common difference is same, the given sequence is an arithmetic sequence.

Hence,

Option 2: Yes, d= 5 is the correct answer

Which number goes in the box?
8 + 9 = 9 +

Answers

Answer:

8

Step-by-step explanation:

I hope this helps you out!

Answer:

8

Step-by-step explanation:

...

Which of the following graphs represents the equation above -3x+2y=8

Answers

Answer:

Is there a picture of the graphs...?

Step-by-step explanation:

Anyways, the answer should be y= 3/2x +4

If you show me the graphs I could possibly help you find which one is correct.

Answer:

Step-by-step explanation:

Here are the graphs, which one goes with

y = 4 + 3/2x ?

Eli's Diner sold 50 milkshakes last week. 60% of the milkshakes had whipped cream on top. How many milkshakes with whipped cream were sold?

Answers

Answer:

30 will be the number of milkshakes had whipped cream on top.

Step-by-step explanation:

Total number of milkshakes sold by Eli's Diner last week = 50

As 60% of the milkshakes had whipped cream on top.

Let x be the number of the milkshakes had whipped cream on top.

[tex]x=\frac{60}{100}\times 50[/tex]

[tex]x=\frac{60}{2}[/tex]

[tex]x=30[/tex]

Therefore, 30 will be the number of milkshakes had whipped cream on top.

Shawn said that in standard notation,
7.142 x 107 will have 7 zeros after the
2 because the exponent is a 7. Is he
correct? Why or why not?

Answers

Answer:

Shawn is incorrect.

Step-by-step explanation:

The decimal is moving 7 places to the right.  The 2 is the third digit, so there will be 4 0s after it.

Pt.2 Please show your work
Find the slope when given the following points
(-3, 2) and (1, 0)

Answers

Answer:

slope is = -1/2

Step-by-step explanation:

y2-y1= 2-0= 2

x2-x1= -3-1= -4

2/-4= -1/2

using the slope formula... y-y
m=___
x-x

it would be 2-0 OVER (fraction formula shown above) -3-1

so your end fraction would be 2/-4 which would be -0.5

so, your slope would be -0.5
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