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
What is the gradient of the graph shown?
sammy [17]

Answer:

-1/2

Because, for every one square, the line goes <em>down </em>by 1/2.

5 0
3 years ago
Read 2 more answers
The sum of two positive numbers is 12. what two numbers will maximize the product g
son4ous [18]

Given two numbers x and y such that:

x + y = 12   ...    (1)


<span>two numbers will maximize the product g</span>

from  equation (1) 

y = 12 - x  

Using this value of y, we represent xy as

xy = f(x)= x(12 - x)

 f(x) = 12x - x^2

Differentiating the above function:

f'(x) = 12 - 2x

Maximum value of f(x) occurs at point for which f'(x) = 0.

Equating f'(x) to 0 we get:

12 - 2x = 0

 2x =  12

> x = 12/2 = 6

Substituting this value of x in equation (2):

y = 12 - 6 = 6

Therefore, value of xy is maximum when:

x = 6 and y = 6

The maximum value of xy = 6*6 = 36

4 0
3 years ago
Help me solve this problem please
Mazyrski [523]

Answer:

Its A

Step-by-step explanation:

4 0
3 years ago
Write the equation in slope-intercept form. 5x+3y=12
Umnica [9.8K]
5x+3y=12
Subtract 5x from both sides
3y=-5x+12
Divide by 3
Y=-5/3x +4
7 0
3 years ago
I need help pls and thank you
Aleks [24]
The fourth table is the correct answer
6 0
3 years ago
Other questions:
  • Can someone please help me
    9·1 answer
  • A trial jury of 6 people will be chosen from among 18 candidates. How many juries are possible? 18,564 742,560 13,366,080 34,012
    10·1 answer
  • Suppose f(x,y,z) = x2 + y2 + z2 and W is the solid cylinder with height 7 and base radius 2 that is centered about the z-axis wi
    12·1 answer
  • For any integer k &gt; 1, the term "length of an integer" refers to the number of positive prime factors, not necessarily distin
    7·1 answer
  • WILL GIVE 30 POINTS AND BRAINLIEST
    13·2 answers
  • Write an equation in point slope form of the line passes through the point (9,0) and has a slope of m=-3
    6·1 answer
  • Which dimensions can create only one unique triangle?
    10·2 answers
  • 4x + 3 Y = 11<br><br><br> Me podrían ayudar por favor a resolverla
    11·1 answer
  • Eexperts can you in step by step none is helping me plz​
    15·1 answer
  • Solve please: (8x)(2y)(3z)​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!