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
prisoha [69]
3 years ago
11

The sum of the first three terms of a sequence is 6 and the fourth term is 16

Mathematics
1 answer:
Sati [7]3 years ago
6 0

Answer:

              a₁ = -5, d = 7,  a₂ = 2, a₃ = 9, a₄ = 16

equation of sequence:    \boxed{\bold{a_n=7n-12}}

Step-by-step explanation:

a₁ + a₂ + a₃ = 6    

a₁ + a₁ + d + a₁ + 2d = 6

3a₁ + 3d = 6

a₁ + d= 2     ⇒ a₁ = 2 - d

a₄ = 16

a₁ + 3d = 16

2 - r + 3d = 16

2d = 14

d = 7

a₁ = 2-7 = -5

a₁ = -5, d = 7   ⇒  a₂ = -5+7 = 2, a₃ = 2+7 = 9, a₄ = 9+7 = 16

equation of arithmetic sequence:

a_n=a_1+d(n-1)\\\\a_n=-5+7(n-1)\\\\\underline{a_n=7n-12}

You might be interested in
A student wrote a photography manual which she plans to sell online for $ 13 per copy. Her total expenses were $ 55. Write a lin
finlep [7]

Answer:

y = 13x - 55

Step-by-step explanation:

So this is what we know

Selling price = $13 per copy

Expenses = $55

The formula for profit in this case is:

Profit = total selling price - expenses

In which y is the profit

The total selling price is 13x. x here is for the number of manuals she sells

The expenses are $55.

This then becomes y =13x - 55

HOPE THIS HELPED

5 0
3 years ago
Write this radical in simplest form:
elena-14-01-66 [18.8K]

Answer:

in simplest form the radical would be, 4 3/4

( the / is supposed to be the square root sign)

hope this helped ;D

8 0
3 years ago
Suppose the mean GPA of all students graduating from a particular university in 1975 was 2.40. The registrar plans to look at re
ycow [4]

Answer:

Correct option:

(B) <em>H₀</em>: <em>μ</em> = 2.40 vs. <em>Hₐ</em>: <em>μ</em> ≠ 2.40.

Step-by-step explanation:

The registrar of particular university in 1975 plans to look at records of students graduating last year to see if the mean GPA has changed from 2.40.

The registrar can use a single mean test to determine whether the mean has changed or not.

The hypothesis can be described as:

<em>H₀</em>: The mean GPA is 2.40, i.e. <em>μ</em> = 2.40.

<em>Hₐ</em>: The mean GPA is different from 2.40, i.e. <em>μ</em> ≠ 2.40.

To perform the test the registrar can either use a <em>z</em>-distribution or a <em>t</em>-distribution.

If the data provided gives some insight about the population standard deviation and the sample selected is quite large then the <em>z</em>-distribution can be used.

Otherwise it is wiser to use a <em>t</em>-distribution.

The decision rule is:

If the <em>p</em>-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

Thus, the correct option is (B).

6 0
3 years ago
What is the domain of a sine function?
Blizzard [7]
Hello there!

The domain of the sine function is [-infinity, +infinity].


I hope this is the answer you were looking for. As always, it is my pleasure to help students like you!
7 0
3 years ago
Read 2 more answers
annie adds 2 spoonfuls of sugar to her tea and sophie adds 3 spoonfuls to her tea. If one spoonful is 4 grams of sugar and a a c
Tresset [83]

240%

Step-by-step explanation:

if there is 240 grams  then you just put a percent sing but are you asking What is the percentage of sugar in each cup? by spoons?

3 0
3 years ago
Other questions:
  • mr perkins has $120 in a savings account. the interest rate is 5% per year and is simple interest. how much will he have in 2 ye
    5·1 answer
  • There are
    10·1 answer
  • What is the point of intersection of these two lines? -4x + y = 8 2x - y = 4 (2, 0)
    6·1 answer
  • A mayor wants to determine if the people in his city think that he is doing a good job.
    9·2 answers
  • PLS MY GRADE IS LOW!! IVE BEEN ASKING SINCE YESTERDAY!! LITTERALLY!!! EXTREAMLY EASY I AM JUST AFRAID TO GET THIS WRONG SO IF YO
    10·1 answer
  • Which choice is equivalent to the fraction below x&gt;=3? ​
    7·1 answer
  • Please help whit ratio
    13·2 answers
  • Use cramer's rule of x-3y+z=13,3x+2y-z=1,5x+7y+2z=9​
    14·2 answers
  • 3(1) to the power of 2
    12·1 answer
  • A 3.0-kg ball moving eastward at 4.0 m/s suddenly collides with and sticks to a 5.0-kg ball moving northward at 3.0 m/s. what is
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!