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
Masja [62]
2 years ago
7

The sum of three consecutive terms of an arithmetic sequence is 27, and the sum of their squares is 293. What is the absolute di

fference between the greatest and the least of these three numbers in the arithmetic sequence?
The answer is 10 but I don’t know how to get it
Mathematics
1 answer:
Ber [7]2 years ago
7 0

The absolute difference between the greatest and the least of these three numbers in the arithmetic sequence is 10.

The sequence is an arithmetic sequence. Therefore,

d = common difference

let

a = centre term

Therefore, the 3 consecutive term will be as follows

a - d,  a, a + d

a - d +  a + a + d = 27

3a = 27

a = 27 / 3

a = 9

Therefore,

(a-d)² + (a)² + (a + d)² = 293

(a²-2ad+d²) + 9² + (a² + 2ad + d²) = 293

(81 - 18d + d²) + 81 + (81 + 18d + d²) = 293

243 + 2d² = 293

2d² = 50

d² = 50 / 2

d = √25

d = 5

common difference = 5

Therefore, the 3 numbers are as follows

9 - 5 , 9, 9 + 5 = 4, 9, 14

The difference between the greatest and the least of these 3 numbers are as follows:

14 - 4 = 10

learn more on Arithmetic progression: brainly.com/question/25749583?referrer=searchResults

You might be interested in
The sum of two numbers is 49 and the difference between these two numbers is 9. What are these two numbers?​Shown working out pl
8_murik_8 [283]

Let numbers be x and y

ATQ

  • x+y=49---(1)

  • x-y=9---(2)

Adding both

\\ \sf\longmapsto 2x=58

\\ \sf\longmapsto x=\dfrac{58}{2}

\\ \sf\longmapsto x=29

Now putting value in eq(2)

\\ \sf\longmapsto x-y=9

\\ \sf\longmapsto 29-9=y

\\ \sf\longmapsto y=20

7 0
3 years ago
What is the sum of the first seven terms of the geometric series? 3 12 48 192 ...
Ad libitum [116K]

Hence, the sum of the given GP is 16347

<h2>What is a series?</h2>

a series is the cumulative sum of a given sequence of terms. Typically, these terms are real or complex numbers, but much more generality is possible.

<h3>How to solve?</h3>

we can identify from the given geomertric series.

first term = a(say) = 3

geometric factor of progression = r(say) = 4

Sum of the first 7 terms = a(\frac{r^n-1}{r-1})          ,where n is 7

Sum = 3(\frac{4^7-1}{3}) = 16348-1

       = 16347

Hence, the sum of the given GP is 16347.

to learn more about series: brainly.com/question/12578626

#SPJ4

8 0
2 years ago
HELPPPP!!!!!
Vesna [10]
The awnser is (3,0)
8 0
3 years ago
Find an equation of the line with an undefined slope and passes through the point (3, -4).
Hatshy [7]
Undefined means it goes through the x intercept, x=3
6 0
3 years ago
If 3x−y=12, what is the value of <br>8x/2y?​
Ulleksa [173]

Answer:

3x-y=12

3x-12=y

to find value of

8x/2y

8x/2(3x-12)

8x/6x-24

8x/6x-8x/24

4/3-x/3

4-x/3

Step-by-step explanation:

4 0
2 years ago
Other questions:
  • In a if P is equals to 3 cm BD is equal to 3.9 CM PQ is equals to 3.6 cm and q f is equals to 2.4 CM state PQ is parallel to EF​
    9·1 answer
  • Which of the figures appear to be congruent?
    7·1 answer
  • a city block is a square with each side measuring 102 yards. Find the length of the diagonal of the city block.
    15·1 answer
  • 49 is 35% of what number? Use percent equation
    6·1 answer
  • Please help with function notation question (see attached file)
    12·1 answer
  • 2. "In a job shop, effective capacity is only 50 percent of design capacity, and actual output is" 80 percent of effective outpu
    10·1 answer
  • Please help so i an pass
    8·1 answer
  • Suppose that it is reported in the news that 12% of the people living and working in Kokomo feel that their commute is too long.
    9·1 answer
  • According to Hinduism, people are reborn into new physical forms. The form one is born into depends on one’s
    11·2 answers
  • Help me please i need it
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!