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
vredina [299]
3 years ago
14

A. [4 marks]

Mathematics
1 answer:
storchak [24]3 years ago
7 0

The value of d is -2

Step-by-step explanation:

The nth term of the arithmetic sequence is u_{n}=u_{1}+(n-1)d , where

  • u_{1} is the first term
  • d is the common difference between each 2 consecutive terms

The nth term of the geometric sequence is u_{n}=u_{1}r^{n-1} , where

  • u_{1} is the first term
  • r is the common ratio between each two consecutive terms r=\frac{u_{2}}{u_{1}}=\frac{u_{3}}{u_{2}}

∵ u_{1} of an arithmetic sequence is 1

∵ The common difference is d, where d ≠ 0

∵ u_{2} , u_{3} , u_{6} are the first 3 terms of a geometric sequence

∵ u_{2} = 1 + (2 - 1)d

∴ u_{2} = 1 + d

∵ u_{3} = 1 + (3 - 1)d

∴ u_{2} = 1 + 2d

∵ u_{6} = 1 + (6 - 1)d

∴ u_{2} = 1 + 5d

∴ The first 3 terms of the geometric sequence are (1 + d) , (1 + 2d) ,

   (1 + 5d)

∵ The common ratio in the geometric sequence is r=\frac{u_{2}}{u_{1}}=\frac{u_{3}}{u_{2}}

∴ r=\frac{1+2d}{1+d}=\frac{1+5d}{1+2d}

- Use cross multiplication with the equal fractions

∵ \frac{1+2d}{1+d}=\frac{1+5d}{1+2d}

∴ (1 + 2d)(1 + 2d) = (1 + d)(1 + 5d)

∴ 1 + 2d + 2d + 4d² = 1 + 5d + d + 5d²

- Add like terms in each side

∴ 1 + 4d + 4d² = 1 + 6d + 5d²

- Subtract 1 from both sides

∴ 4d + 4d² = 6d + 5d²

- Subtract 4d from both sides

∴ 4d² = 2d + 5d²

- Subtract 4d² from each side

∴ 0 = 2d + d²

- Take d as a common factor

∴ 0 = d(2 + d)

- Equate each factor by 0

∴ d = 0 but we will reject it because d ≠ 0

∴ 2 + d = 0

- Subtract 2 from both sides

∴ d = -2

The value of d is -2

Learn more:

You can learn more about the sequence in brainly.com/question/1522572

#LearnwithBrainly

You might be interested in
Omg please help for brainlist !!!!!!!!!!!!!!!!!!!
zhannawk [14.2K]

Answer:

f(x) is linear

g(x) is exponential

Step-by-step explanation:

A linear function will always have the same rate of change between equally distant points, while an exponential function will have an increasingly large rate of change between equally distant points.

First, look at f(x). All these points are equally distant at 2 units apart on the x-axis, so they can be directly compared:

(-38)-(-18)=-20\\(-58)-(-38)=-20\\(-78)-(-58)=-20

All of these points are the same distance apart on the y, so f(x) must be a linear function.

Now look at g(x). These are also all equally distant at only 1 unit apart.

30-10=20\\90-30=60\\270-90=180

These are very clearly not the same distance apart on the y, so g(x) must be the exponential function.

6 0
2 years ago
A company makes video games. The price of a video game is modeled by the function p(x) = 30x + 2, where x is the number of years
atroni [7]

The answer is option C "multiplication." You have the function p(x) = 30x + 2 and x equals the number of years since the company started producing games which has this equation also s(x) = 500x + 250 in order to find the revenue from their video games the company should use the multiplication on the polynomials.

Hope this helps!


4 0
3 years ago
Read 2 more answers
Which expression has a value of 16 when x=2
ELEN [110]

Answer:

Step-by-step explanation:

point sorry

7 0
2 years ago
Oscar has a gift card with a $110 balance. He buys several video games that cost $15 each. After the purchases, his gift card ba
True [87]

Answer: Um... Not quite sure what you're asking, but he bought about 5 games with the gift card.

6 0
3 years ago
Read 2 more answers
What’s the slope and y - intercept of this equation ?
zavuch27 [327]

Answer:

Slope = -\frac{7}{3}

Y-intercept = 4

Step-by-step explanation:

-> See attached

-> This equation is in slope-intercept form.

         [] When we use y = mx + b, the m is the slope and the b is our y-intercept.

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather

5 0
2 years ago
Read 2 more answers
Other questions:
  • Whats the slope of (-3,-2) and (5,4)
    14·2 answers
  • What is x in 2(x+6)=14
    13·1 answer
  • How many trout are estimated to be present if a random sample of 5,000 fish is collected from the lake?
    10·2 answers
  • An optical inspection system is used to distinguish among different part types. The probability of a correct classification of a
    15·1 answer
  • Explain when you would not need to regroup any hundreds into thousands when multiplying a 4 digit number by a 1 digit number.
    8·1 answer
  • Round the values below to the nearest hundredths
    11·2 answers
  • 2 poin
    6·2 answers
  • Solve for x <br> -4x+6(6-2x)=-7-36<br> A) 8<br> B) 15<br> C) -7<br> D) 3
    7·1 answer
  • The answer to a word problem should always include which of the following
    11·2 answers
  • What is the finance charge for a balance of 350.55 at a annual rate of 18%?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!