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
Veronika [31]
3 years ago
5

The first term of an arithmetic sequence is 7 and the sixth term is 22. Find(a)the common difference;(2)(b)the twelfth term;(2)(

c)the sum of the first 100 terms.
Mathematics
1 answer:
SVEN [57.7K]3 years ago
7 0

d = 3 , a₁₂ = 40 and Sx_{100} = 7775

In an arithmetic sequence the nth term and sum to n terms are

<h3>• an = a₁ + (n-1)d</h3><h3>• S_n = \frac{n}{2}[2a + (n-1)d]</h3><h3>where d is the common difference</h3><h3>a₆ = a₁ + 5d = 22 ⇒ 7 + 5d = 22 ⇒ 5d = 15 ⇔ d = 3</h3><h3>a₁₂ = 7 + 11d = 7 +( 11× 3) = 7 + 33 = 40</h3><h3>S₁₀₀ = \frac{50}{2}[(2×7) +(99×3)</h3><h3>       = 25(14 + 297) = 25(311)= 7775</h3>
You might be interested in
What is the OUTPUT if the input to the equation y=2x - 7 is x =4?
mariarad [96]

Answer:

the output is y=1

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
What is the interquartile range of this data set?
olasank [31]
The answer would be 46 (55-9=46)
3 0
3 years ago
Read 2 more answers
What number is 30 percent of 50
choli [55]

Answer:

15 (50*0.3)

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
As an airplane rises, the outside temperature drops 3.6 degrees Fahrenheit for each 1000 feat of elevation gain. Suppose the out
VLD [36.1K]

Answer:

30000 feet

Step-by-step explanation:

temperature on ground level = 65 °F

temperature at cruising altitude = -43 °F

total decrease in temperature = 65 - (- 43) = 65 + 43 = 108 °F

for each 1000 feet elevation temperature drops by 3.6 °F

and we have the total drop of temperature as 108 °F.

so,  Height of plane at cruising altitude = (drop in temperature/ 3.6) X 1000

                                                                 =\frac{108}{3.6} X 1000

                                                                 = 30000 feet

7 0
4 years ago
HELP PLEASE THANK YOU! :) 50 POINTS !!!!!!!1
a_sh-v [17]

Answer:  0.88

Step-by-step explanation:  

Let C is the event of drinking coffee, T is the event of drinking tea and M is the event of drinking milk.

Thus, when we make the Venn diagram of the given situation according to the given information,

Total number of people = 50

Number of people who like coffee, tea and milk = 19

Number of people who like coffee, tea but not milk = 16

Number of people who like coffee, milk but not tea = 2

Number of people who like tea, milk but not coffee = 5

Thus, the number of people who like tea only = Total people - (people who like coffee, tea but not milk + people who like coffee, tea and milk + the one who only like tea and milk but not coffee)

= 50 - ( 16 + 19 + 5) = 50 - 46 = 4

Thus, Total number of the person who like milk = 16 + 19 + 5 + 4 = 44

⇒ Probability that this person likes tea = \frac{\text{ Total person who like to drink milk}}{\text{ Total number of people}} = \frac{44}{50} = 0.88





3 0
4 years ago
Other questions:
  • Three coins are tossed at the same time what is the probability that exactly 2 heads appear
    6·1 answer
  • Select the function that represents a geometric sequence.
    11·2 answers
  • What is the value of x?<br><br><br><br> Enter your answer in the box.<br><br> x =
    12·2 answers
  • What elephant's weight is 2.85 tons when rounding to the nearest hundredth?
    9·1 answer
  • Which box-and-whisker plot represents this data: 6,7,9,9,20,22,26,28,29,30?
    11·1 answer
  • The legs of a isosceles right triangle both measures 10 inches find the lenth of the hypotenuse
    6·1 answer
  • There are 80 students total in 7th grade, of whom 15% are left handed. How many
    12·1 answer
  • I put C but again I’m not really sure it’s the correct answer.
    8·1 answer
  • Which is a true statement about the graph of Y= -1/3x -6?
    14·2 answers
  • Solve -6.5m+14.3&lt;-22.75
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!