1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
babymother [125]
3 years ago
15

What is the sum of the first 30 terms of the arithmetic series 27,32,37,42,47

Mathematics
1 answer:
AlladinOne [14]3 years ago
3 0

Answer:

2985

Step-by-step explanation:

The formula for the sum of an arithmetic series is given by the formula:

S=\frac{k}{2}(a+x_k)

Where k is the number of terms, a is the first term, and x_k is the last term. In this case, the last term is the 30th term because we are finding the sum of the first 30 terms.

So, we need to find the 30th term. To do so, we can write an explicit formula for our sequence.

The standard form for an arithmetic sequence is given by the formula:

x_n=a+d(n-1)

Where a is the initial term and d is the common difference.

From our sequence, we can see that the initial term a is 27. The common difference is 5 because each term is 5 greater than the previous one.

So, our equation is:

x_n=27+5(n-1)

So, to find the 30th term, substitute 30 for n:

x_{30}=27+5(30-1)

Subtract:

x_{30}=27+5(29)

Multiply:

x_{30}=27+145

Add:

x_{30}=172

So, the 30th term is 172.

Now, substitute this into our original sum formula:

S=\frac{k}{2}(a+x_k)

Substitute 30 for k (the amount of terms), 27 for a (the first term), and 172 for x_k (the 30th and last term). So:

S=\frac{30}{2}(27+172)

Reduce and add:

S=15(199)

Multiply:

S=2985

So, the sum of the first 30 terms is 2985.

You might be interested in
2. Find the value of x.<br> (1 point)<br> (5x)<br> (3x+28)<br> O 14<br> O20<br> O 12<br> O 19
nata0808 [166]

Answer:

x = 14

Step-by-step explanation:

The triangle has 2 congruent legs and is isosceles with 2 base angles being congruent , then

5x = 3x + 28 ( subtract 3x from both sides )

2x = 28 ( divide both sides by 2 )

x = 14

6 0
3 years ago
The number of words Latisha can text, y,
lyudmila [28]

Answer for A it’s 24

6 0
2 years ago
What is 4(x−2)=3(2y−1) in standard form?
exis [7]

Answer: 4x-6y=5

Step-by-step explanation: Using the formula, Ax+By=C, write the equation in standard form.

Hope this helps you out! ☺

8 0
3 years ago
Whats this answer i need it fast uwu
IrinaVladis [17]
Find slope (y2-y1)/(x2-x1)
Pick points: (1,10) , (2,8)
(8-10)/(2-1) = -2/1 = -2
Y = -2x + b
10 = -2 + b, b = 12
It would be the first response
12 = initial while -2 is rate of change
3 0
2 years ago
A bakery sold a total of 3028 coffee buns and blueberry buns. 1560 more coffee buns were sold than the blueberry buns. How many
Natali [406]

Answer:

\large{ \tt{ -  \: HEY  \: AH~\:♡ }}

\large{ \tt{✺ \: SOLUTION}} :

  • Provided : Total sold bakery items : 3028 coffee buns and blueberry buns & 1560 more coffee buns were sold than the blueberry buns.

  • To find : Number of coffee buns the bakery sold

- First , Subtract 1560 from 3028 :

\large{ \tt{→ \: 3028 - 1560 = 1468}}

We just subtacted the number of more coffee buns from the number of told items sold which means that the number of coffee buns and the number of blueberry buns sold are equal for now. Now divide 1428 by 2 :

\large{ \tt{→ \frac{1428}{2} = 734 }}

Now - Let's get back to the second sentence of the question and add 734 & 1560 :

\large{ \tt{→ \: 734 + 1560 =  \large{ \boxed{2294}}}}

  • Hence , The bakery sold 2294 coffee buns.

- Hope this helps , oneesan! ;)

7 0
2 years ago
Other questions:
  • 50 points !! please help hurry
    7·2 answers
  • For each reaction between a ketone and an amine, draw the curved arrow(s) to show the first step of the mechanism, then draw the
    9·1 answer
  • For a two week period, John and Amanda had the following transactions occur to their checking account: a deposit of $1,644.50; c
    15·1 answer
  • When taking a long road trip, plan rest stops before you leave - at least once every __________
    7·1 answer
  • 5. Suppose a population of 500 crickets doubles in size every month. How
    14·1 answer
  • The probability ofwinning a game is 25%. How manytimes
    12·2 answers
  • Please help with the math problem shown in the image
    13·2 answers
  • Please help lolz!! ill give brainly &lt;3
    9·1 answer
  • Name all things on the list that are renewable or nonrenewable
    10·2 answers
  • GUYSSSSS!!!! PLEASE I NEED HELP RIGHT NOWW!!! HELP PLEASE!​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!