Find sum of arithmetic series where a1 = 7, n=31, nth a =127

Answers

Answer 1

Answer:

Sum of arithmetic series is [tex]2077[/tex]

Step-by-step explanation:

We have [tex]n[/tex]th term of arithmetic sequence

[tex]a+(n-1)d[/tex]

Here

[tex]a+(n-1)d=127\\\\7+(31-1)d=127\\\\d=\frac{120}{30} \\\\=4[/tex]

Sum of arithmetic sequence [tex]=\frac{n}{2} (2a+(n-1)d)[/tex]

[tex]=\frac{31}{2} (2\times7+(31-1)4)\\\\=\frac{31}{2} (14+120)\\\\=31\times67\\\\=2077[/tex]

Answer 2

Answer:

The sum of arithmetic series is 2077.

Step-by-step explanation:

Solution :

Here we have provided that :

»» [tex]\rm{a_1}[/tex] = 1»» [tex]\rm{n}[/tex] = 31»» [tex]\rm{a_n}[/tex] = 127

We need to find :

»» The sum of arithmetic series.

Here's the required formula to find the sum of arithmetic series :

[tex]\longrightarrow{\pmb{\sf S = \dfrac{n}{2} \Big(a_1 + a_n \Big)}}[/tex]

Substituting all the given values in the formula to find the sum of arithmetic series :

[tex]{\longrightarrow{\sf S = \dfrac{n}{2} \Big(a_1 + a_n \Big)}}[/tex]

[tex]{\longrightarrow{\sf S = \dfrac{31}{2} \Big(7 + 127 \Big)}}[/tex]

[tex]{\longrightarrow{\sf S = \dfrac{31}{2} \Big(134 \Big)}}[/tex]

[tex]{\longrightarrow{\sf S = \dfrac{31}{2} \times 134 }}[/tex]

[tex]{\longrightarrow{\sf S = \dfrac{31}{\cancel{2}} \times \cancel{134 }}}[/tex]

[tex]{\longrightarrow{\sf S = 31 \times 67}}[/tex]

[tex]{\longrightarrow{\sf S = 2077}}[/tex]

[tex]\star \: {\underline{\boxed{\sf{\red{S = 2077}}}}}[/tex]

Hence, the sum of arithmetic series is 2077.

[tex]\rule{300}{1.5}[/tex]


Related Questions

A computer processes information in nanoseconds. A nanosecond is one-billionth of a second. Write this number as a decimal.

Answers

Answer:

0.000000001

Step-by-step explanation:

Let's convert this :

0.000000001

  tHT      M    B

t=tenths

H=Hundredths

T=Thousandths

M=millionths

B=Billionths

I have no idea how to do this. Please help. ​

Answers

Answer:

Area is 5 cm and perimeter is 12 cm

Step-by-step explanation:

Area: top left sqare:

1cm * 1cm = 1 cm

bottom rectangle:

1cm * 3 cm = 3 cm

top right square:

1cm * 1cm = 1 cm

Perimeter:

1 cm + 2 cm+ 3 cm+ 2 cm+ 1 cm + 1 cm + 1cm + 1cm  = 12 cm

pls help. i don't like math

Answers

Answer:

X = 5 3/8 (5 and 3 eighths)

Step-by-step explanation:

4/5x = 5 1/5 - 9/10

4/5x = 43/10

x=43/8

x= 5 3/8

Answer:

Exact Form: x=43/8

Decimal Form: 5.375

Mixed number form: x= 5 and 3/8

Step-by-step explanation: here is the steps

Find the solutions to x2 = 24.
A. x = 16.2
X
B. X= 14,6
C. X= +6.14
D. X = +216

Answers

I think it’s c, am not shuree tho

What is the area, in square centimeters, of the trapezoid below?

Answers

Answer:

36 cm²

Step-by-step explanation:

1/2 × (8.9+5.5) ×5.5

1/2×14.4×5.5

1/2×72

36 cm²

i need help assap

Consider the function g(x) shown below over a domain of [1,∞).

g(x) = 2(x – 1)2 – 3

Part A
Determine g–1(x).


Part B
Identify the domain and range of g(x) and g–1(x). Represent the domains and ranges in inequality, interval, and set notation. Describe the relationship between the domains and ranges of g(x) and g–1(x).


Part C
Graph g(x) and g–1(x). Describe the relationship between the graphs of g(x) and g–1(x).

Answers

It’s 2=x because you have start with 2 then 5

express the following fractions as the sum or difference of two fractions (x^2+y^2)/x^4

Answers

Answer:

 [tex]\frac{1}{x^2}[/tex] + [tex]\frac{y^2}{x^4}[/tex]

Step-by-step explanation:

[tex]\frac{x^2 + y^2}{x^4}[/tex] = [tex]\frac{x^2}{x^4}[/tex] + [tex]\frac{y^2}{x^4}[/tex] = [tex]\frac{1}{x^2}[/tex] + [tex]\frac{y^2}{x^4}[/tex]

The solution of the expression (x²+y²)/x⁴ is [(1/x² + y²/x⁴)].

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The given expression is  (x²+y²)/x⁴. The expression will be solved as,

E =  (x²+y²)/x⁴

Separate the terms into two fractions,

E =  (x²+y²)/x⁴

E = (x²/x⁴) + ( y² / x⁴)

Divide the divisible terms and solve,

E = (1/x² + y²/x⁴)

To know more about an expression follow

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#SPJ2

What is the common denominator of StartFraction 1 Over a EndFraction StartFraction 1 Over b EndFraction in the complex fraction StartFraction 1 Over a EndFraction minus StartFraction 1 Over b EndFraction divided by StartFraction 1 Over a EndFraction 1 Over b EndFraction?.

Answers

The common denominator is 1

Given the expression:

[tex]\frac{1/a-1/b}{1/a1/b}[/tex]

Find the LCM of the numerator to have:

[tex]\dfrac{\frac{b-a}{ab} }{\frac{1}{a} \frac{1}{b} }[/tex]

Simplify both the numerator and the denominator to have:

[tex]= \dfrac{\frac{b-a}{ab} }{\frac{1}{ab} }\\= \frac{b-a}{ab} \times ab\\=\frac{b-a}{1} \times 1 \\=\frac{b-a}{1}[/tex]

From the result, we can see that the common denominator is 1

Learn more about fractions here: https://brainly.com/question/17743912

Answer:

here is the correct answer for edge2022

Step-by-step explanation:

HELP!! BRAINLIEST!! +15 POINTS!! REAL ANSWERS ONLY PLEASE

Answers

Lol that’s so easy haha

Given that m||n, determine the relationship between ∠9 and ∠15.

Answers

The relationship between ∠9 and ∠15 is (c) alternate exterior angles.

There are several relationships that can be formed by angles within the transversal of parallel lines.

From the attached figure, we can see that angles ∠9 and ∠15 are exterior angles of parallel lines m and n.

Because these lines are parallel, then both angles are alternate exterior angles.

Read more about parallel lines at:

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Alebgra!!

Please help me fast now plzzzzzzzzzzzzzzzzzzzzzzzzzzzzz i will give you alot of my points.

Question:

Find the perimeter of the rectangle with length (2w + 7) feet and width w feet.

Answers

Answer:

I think it's 18

Step-by-step explanation:

P=2(l+w)=2(7+2)=18

it's been awhile I believe this is it

Perimeter is the sum of all the sides
A rectangle has four sides=2L+2W

2(2w+7)+2w
4w+14+2w
=6w+14

Please mark as brainliest if it’s correct

Solve please in need of help

Answers

Answer:

not clear and I don't know the answer

jack has $37 and saves $6.50 per week diane has $9 and saves $8.25 per week write and solve an equation to find out how many weeks it would take for jack and diane to have saved the same amount of money

Answers

37+6.5= 9+8.25x
-1.75x = 28
X= 16

how do you solve 9r=3r+6

Answers

9r=3r+6
Subtract 3r from both sides
6r=6
Divide both sides by 6
r=1

Answer:

r=1

Step-by-step explanation:

9r=3r+6  

-3r -3r

6r=6

/6  /6

r=1

Check your answer:

9(1)=3(1)+6

9=9 ✔️

helpp my grades are almost dueeeeeeee,,, but anyway hows yall dayyy?

Answers

C is the. Answer as you multiply by -1/3

Answer: c) -1/6, check picture below

Step-by-step explanation:

answer this
1) Singapore is located in the +8 time zone. An aeroplane departs from Singapore at 3.00 p.m. (15:00) on Monday and travels across the IDL to Honolulu located in the
-10 time zone. If it takes 12 hours for the journey, find the local time and date when it arrives in Honolulu.



2)An aeroplane departs from Dawson located in the -8 time zone at 6:00 a.m. on
Monday, flies across the IDL and arrives in Tokyo (Japan) in the +9 time zone.
If the flight arrives in Tokyo at 4.00 p.m. on Tuesday, find the time taken for the
journey

Answers

Answer:

Local Time = 9:00

Date = Monday

Step-by-step explanation:

Singapore is located in the +8 time zone. An aeroplane

departs from Singapore at 3.00 p.m. (15:00) on Monday

and travels across the IDL to Honolulu located in the

-10 time zone. If it takes 12 hours for the journey, find

the local time and date when it arrives in Honolulu

quick pls!! my math grade is at a B! I need to raise it.

Answers

I don’t know but I think it should be -04 I assume don’t know

17) The growth of a certain bacteria colony is modeled by the function y = 100(1.20)*. Which statements are
correct?
A)
B)
100 is the initial number of bacteria.
x is the growth factor.
This is an exponential function.
1.20 is the number of time intervals.
D)
E)
y equals the final number of bacteria.
C)

Answers

Answer:

the corect answers is d and c

Step-by-step explanation:

Answer: B D E

Step-by-step explanation: I got it right on usetestprep

please help will give brainliest

Answers

Answer:

Look at the pictures (they are color coded)

red is 1st

blue is 2nd

green is 3rd

black is 4th

Examine the function f(x)=log2x.
Which point is the intersection of f(x) and the line y=1?

(1,2)
(12,1)

(2,1)
(1,1)

Answers

Answer:

Is the question worded properly?

I find the intersection of the two lines to be (5,1), which is not an answer option.

Step-by-step explanation:

We want the value of x that will produce a value of 1, which will be the point the curve crosses y = 1.  

log (10) = 1

Therefore 2x = 1, and x = 5

(5,1)

What is the value of the expression?

(514−212)+(623−312)

Enter your answer as a mixed number in simplest form by filling in the boxes.

Answers

Answer:

[tex] = { \rm{(514 - 212) + (623 - 312)}} \\ \\ = { \rm{(302) + (311)}} \\ \\ ={ \underline{ \: \: {}^{ - } 9 \: \: }}[/tex]

What do the following two equations represent?
. 4x + 2y = 10
• 4x – 2y = –10
Choose 1 answer:
The same line
Distinct parallel lines
Perpendicular lines
Intersecting, but not perpendicular lines

Answers

Answer:

Intersecting but not perpendicular

Step-by-step explanation:

2y=-4x+10= Y=-2x+5

-2y=-4x-10= Y=2x+5

15a. Cindy can make $100 in four days babysitting. At that rate, how many day will it take
her to make $425.

Answers

Answer:

4.2

Step-by-step explanation:

Suppose line g is the line with equation y=x. Given ​A(6​,-2​), ​B(​6,3​), and C(-2,-6), what are the coordinates of the vertices of A'B'C' for the reflection?
NEED ANSWER ASAP
Rg

Answers

Answer:

A'(-2, 6)B'(3, 6)C'(-6, -2)

Step-by-step explanation:

Reflection across the line y=x swaps the x and y coordinates:

  (x, y) ⇒ (y, x)

The image points are ...

  A(6, -2) ⇒ A'(-2, 6)

  B( 6, 3) ⇒ B'(3, 6)

  C(-2, -6) ⇒ C'(-6, -2)

4 divided by 3220 pls help me due in 2 hours

Answers

Answer:

1/805

Step-by-step explanation:

4/3220 = 1/805 = 0.00124223....

Solve the literal equation for Y:

4=5x+6y

Answers

Answer:

y=2/3-5x/6

Step-by-step explanation:

what is the answer to 4 3/4 minus 1/3?? Plzz Respond by Tmrw ill give 45 points and brainliest

Answers

Answer:

53/12

Step-by-step explanation:

Conversion a mixed number 4 3/

4

to a improper fraction: 4 3/4 = 4 3/

4

= 4 · 4 + 3/4

= 16 + 3/

= 19/

4

To find a new numerator:

a) Multiply the whole number 4 by the denominator 4. Whole number 4 equally 4 * 4/

4

= 16/4

b) Add the answer from previous step 16 to the numerator 3. New numerator is 16 + 3 = 19

c) Write a previous answer (new numerator 19) over the denominator 4.

Four and three quarters is nineteen quarters

Subtract: 19/

4

- 1/

3

= 19 · 3/

4 · 3

- 1 · 4/

3 · 4

= 57/12

- 4/12

= 57 - 4/12

= 53/12

Write ratios in the form 1:n or n:1 6 : 14

Answers

Answer:

3/7 : 1 OR 1 : 7/3

Step-by-step explanation:

You can set up ratios as a fraction and solve for the missing piece. See images.

Answer:

1 : 2.33 aka 1: 2 1/3

Step-by-step explanation:

1) 6 : 14

2) divide both sides by 6

6/6=1

14/6=2 1/3

3) 1 : 2 1/3

What is the following product? Assume x greater-than-or-equal-to 0 (4 x StartRoot 5 x squared EndRoot 2 x squared StartRoot 6 EndRoot) squared.

Answers

The simplified expression for the product [tex](4x\sqrt{5x^2} )(2x^2\sqrt{6})[/tex] is:

[tex]8\sqrt{30} x^4[/tex]

The given expression is:

[tex](4x\sqrt{5x^2} )(2x^2\sqrt{6})[/tex]

Note that :

[tex]\sqrt{5x^2} = x\sqrt{5}[/tex]

The given expression can then be re-written as:

[tex](4x^2\sqrt{5} )(2x^2\sqrt{6})[/tex]

Multiplying like terms together:

[tex]8x^4\sqrt{30}[/tex]

Finally, the resulting expression can be written as:

[tex]8\sqrt{30} x^4[/tex]

Learn more here: https://brainly.com/question/25913492

Answer:

D 104 x Superscript 4 + 16 x Superscript 4 Baseline StartRoot 30 EndRoot

Step-by-step explanation:

Edg 2022

Find 85 - 72 x 4 ÷ 2 (13 - 11)

Answers

Answer:

13

Step-by-step explanation:

using BODMAS

13-11=2

SO 2*2=4

4/4=1

1*72=72

THEREFORE it is 85-72 =13

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