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
Which equation represents a line which is parallel to the x-axis?
Allushta [10]

Answer:

y = 8

Step-by-step explanation:

The equation of a line parallel to the x- axis has equation

y = c

where c is the value of the y- coordinates the line passes through.

Then

y = 8 ← is equation of line parallel to the x- axis

3 0
2 years ago
The owner of an apartment complex is preparing a report about the property. he wants to show how the number of available apartme
Stella [2.4K]
B - line graph. A line graph should be added because he wants to know how many of available apartments there were during the time of the year and line graphs are usually up and down on the info. 
3 0
3 years ago
Read 2 more answers
Which linear equation passes through the point (10,-7)
N76 [4]
Y = -7
or
x = 10
or
y = x - 13
there can be endless answers
8 0
2 years ago
Read 2 more answers
The graph of △ABC has coordinates A(−3, −1), B(−4, −4), and C(−1, −2)
erik [133]

Answer:  

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Eeeek help, I don’t exactly know how to calculate the width of the missing shape!
Anuta_ua [19.1K]

Answer:

Perimeter = 101.2 cm

Step-by-step explanation:

The given figure has a length of 18 cm and width of 24 cm.  A rectangle of length 8.6cm has been cut out, however, the question is asking to find the perimeter, or distance around the figure.  The overall rectangle still has a perimeter of 18 + 18 + 24 + 24 = 84. However, now it also has two additional sides of 8.6cm each, so 8.6 + 8.6 = 17.2.  

Add all the sides together for perimeter:

84 + 17.2 = 101.2 cm

8 0
3 years ago
Other questions:
  • Using basic trigonometric identities simplify the
    8·1 answer
  • Please solve<br>x^2+x-6006=0​
    11·1 answer
  • Problem 4. Prove that log, 11 is irrational (15 pts) Answer:
    14·1 answer
  • Brittany is at a restaurant. Her bill is $48 plus 15%. She gave an $100. How much did she get back?
    15·2 answers
  • Find the value of each expres<br> 1. (-3)(-2) + 8
    6·1 answer
  • Which of the following linear equations passes through points (-1, 5) and (1, -5)?
    13·1 answer
  • Congruent figure help please :)
    11·1 answer
  • What is 7-(-19)-18(-19)+18
    5·1 answer
  • Please Help me solve this problem
    13·1 answer
  • If m∠ADB=(6x−4)° and m∠BDC=(4x+24)°, find the value of x such that ∠ADC is a right angle.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!