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
Heights (in centimeters) and weights (in kilograms) of 7 supermodels are given below. Find the regression equation, letting the
Delvig [45]
The regression equation:
y = m x + b
m = ( 57 - 50 ) / ( 178 - 168 ) = 7 / 10 = 0.7
50 = 0.7 * 168 + b
50 = 117.6 + b
b = 50 - 117.6
b = - 67.6
y = 0.7 * x - 67.6
The graph is in the attachment.
The weight of supermodel who is 171 cm tall:
y = 0.7 * 171 - 67.6 = 119.7 - 67.6 = 52.1 kg
Download docx
6 0
3 years ago
2y+3=-2x written in slope intercept form
Alex777 [14]
Y=-x-3/2
That's it written in slope intercept form
3 0
3 years ago
Rewrite 4.4.6.4.4.6 using exponents<br>​
kondaur [170]

Answer:

4^{4}×6^{2}

Step-by-step explanation:

There is 2 of the same number 6 and there is 4 of the number 4

I hope this helps

6 0
3 years ago
0.3 x 103<br>0 3 x 1025<br>Write the following as an ordinary number. [<br>(1 Point<br>3x10​
Ne4ueva [31]
0.3 x 103 = 30.9
0.3 x 1025 = 307.5

3 x 10^5 = 300,000
3 0
3 years ago
How to turn a percentage into a decimal
BigorU [14]

Answer:

Divide a percent by 100 and remove the percent sign to change it  from a percent to a decimal.

Step-by-step explanation:

1. Example: 9 % is 0.09

2. Example: 8% is 0.08

3 .Example: 10% will change to 10/100 =decimal 0.10

That how it work just follow the example

7 0
3 years ago
Read 2 more answers
Other questions:
  • Let v1=(2,-6) and v2=(-4,7)
    10·1 answer
  • A skier skis along a circular ski trail that has a radius of 1.25 km. The skiier starts at the East side of the ski trail and tr
    10·1 answer
  • How to simplify 20/10
    11·1 answer
  • Guys i really need your help i have this awesome friend who is cool sometimes but she calls me names and pretends to like me bot
    11·2 answers
  • Which of the following is the simplified version of 3(x + 5) - 6x = 23?
    14·2 answers
  • Please helppp
    15·2 answers
  • PLEASE HELP RN!!!!!!!!!
    11·1 answer
  • 8ftx4ftx5ft what is the diameter
    11·1 answer
  • Every week at the Cougar Scouts meeting, Diane is in charge of the craft activity. This week, she decides to make pinecone bird
    14·1 answer
  • What is the ordered pair? I need help ASAP.
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!