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
True [87]
3 years ago
14

The first two terms of an arithmetic progression are 27 and 24 respectively. How many terms of the progression are to be added t

o get - 30?
Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
4 0

Answer:

20 terms

Step-by-step explanation:

<u>Given AP with the first two terms:</u>

  • a₁= 27 and a₂=24

<u>Common difference: </u>

  • d= 24-27 = -3

<u>To find </u>

  • n for which Sₙ= -30
<h3>Solution</h3>
  • Sₙ = 1/2*n*(a₁+aₙ) =
  • 1/2n(a₁+a₁+(n-1)d) =
  • 1/2n(27+27+(n-1)(-3))=
  • 1/2n(54 - 3n + 3) =
  • 1/2n(57 - 3n)

<u>Since Sₙ = -30</u>

  • 1/2n(57 - 3n) = -30
  • 57n - 3n² = -60
  • 19n - n²- 20 = 0
  • n² -19 n -20= 0

<u>Solving the quadratic equation we get:</u>

  • n =20

So the sum of 20 terms will add up - 30

You might be interested in
2x - 5 = 7
Katyanochek1 [597]

Answer:

6

Step-by-step explanation:

See image below:)

7 0
2 years ago
Read 2 more answers
3^x=1/9<br><br> What does x equal?
Nastasia [14]

Answer: The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable, but we can work out its value if we try!

Step-by-step explanation:

7 0
3 years ago
4h+8=20 what is h?..........
sergey [27]
I believe it's 3 because 4 times 3 equals 12 and 12 plus 8 equals 20! 
4(3)+8=20

Hoped this helped! :)
3 0
3 years ago
Read 2 more answers
When did the nfl start
Radda [10]
The NFL started August 20, 1920
4 0
3 years ago
Read 2 more answers
Elsa, Ryan, and Bill have a total of $135 in their wallets. Ryan has 4 times what Bill has. Elsa has $9 more than Bill. How much
NNADVOKAT [17]

Answer:

Bill has $21.

Step-by-step explanation:

There's $135. 84/4=21. At the same time, 21+9=30. 30+21+84=135.

6 0
3 years ago
Other questions:
  • Sam draws two polygons that are similar. The first polygon has a perimeter of 16 cm and the second polygon has a perimeter of 10
    9·1 answer
  • A roped-off area of width x is created around a 30- by 10-foot rectangular museum display of Native American artifacts. The comb
    9·1 answer
  • Solve each two step equation
    6·2 answers
  • Which linear equation represents a non-proportional relationship? A) y = 10x B) y = 0.75x C) y = −x D) y = 0.25x + 2
    15·2 answers
  • (Only number one) !!PLEASE EXPLAIN HOW TO SOLVE DON’T JUST TELL ME THE ANSWER!!
    9·1 answer
  • PLS HELP ITS MY FINAL EXAM What is the area of the base of the cone below? A cone with height 12 feet and volume 90 feet cubed.
    13·1 answer
  • Xm = np , for x Can I get help?
    15·2 answers
  • Evaluate hj - h, if h = 4 and j = 6.
    9·1 answer
  • Can some one help me with this, I can't get it, and i'll give brainliest, 5 star, and all the good stuff.
    12·1 answer
  • PLEASE HELP I REALLY NEED IT WHAT IS 10% OF 75
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!