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
charle [14.2K]
3 years ago
15

Which of the following is a geometric series? 40 + 50 + 60 + 70 40 + 42 + 44 + 46 40 + 80 + 40 + 120 40 + 20 + 10 + 5

Mathematics
1 answer:
Aloiza [94]3 years ago
7 0

Answer:

40 + 20 + 10 + 5 is a geometric series

Step-by-step explanation:

* Lets revise the geometric series

- There is a constant ratio between each two consecutive numbers

- Ex:

# 5  ,  10  ,  20  ,  40  ,  80  ,  ………………………. (×2)

# 5000  ,  1000  ,  200  ,  40  ,  …………………………(÷5)

* General term (nth term) of a Geometric Series:

∵ U1 = a  ,  U2  = ar  ,  U3  = ar2  ,  U4 = ar3  ,  U5 = ar4

∴ Un = ar^n-1, where a is the first term , r is the constant ratio

  between each two consecutive terms , and n is the position of

  the term in the series

* Now lets check the answers to find the correct one

# 40 + 50 + 60 + 70

∵ 50/40 = 5/4

∵ 60/50 = 6/5

∵ 5/4 ≠ 6/5

- No common ratio between each two consecutive terms

∴ Not geometric series

# 40 + 42 + 44 + 46

∵ 42/40 = 21/20

∵ 44/42 = 22/21

∵ 21/20 ≠ 22/21

- No common ratio between each two consecutive terms

∴ Not geometric series

# 40 + 80 + 40 + 120

∵ 80/40 = 2

∵ 40/80 = 1/2

∵ 2 ≠ 1/2

- No common ratio between each two consecutive terms

∴ Not geometric series

# 40 + 20 + 10 + 5

∵ 20/40 = 1/2

∵ 10/20 = 1/2

∵ 5/10 = 1/2

- There is a common ratio between each two consecutive terms

∴ 40 + 20 + 10 + 5 is a geometric series

You might be interested in
Simplify to create an equivalent expression 19−6(−k−2)
Nikolay [14]
<span>19 − 6( − k − 2) 

Distribute -6:
= 19 + 6k + 12

Combine like terms:
= 6k + 31

Answer: </span>6k + 31
6 0
2 years ago
Read 2 more answers
Which of these triangles appears not to be congruent to any others shown
IRISSAK [1]

Answer: Triangle B

Step-by-step explanation: Congruent just means which shape matches the others, like as you see D and F are congruent as well as A, C, and E.

8 0
2 years ago
Read 2 more answers
Find q if p = -12 and the quotient p/q = -3.
Klio2033 [76]

Answer:

The answer is B) 4

Explanation:

A negative times a negative equals a positive so options A and C are wrong.

-12 divided by 1/4 equals -48

7 0
3 years ago
Read 2 more answers
HI PLEASE HELP ME WITH MY CALCULUS 1 HW? I AM REALLY STUCK. I need help with parts d,e,g.
asambeis [7]

(d) The particle moves in the positive direction when its velocity has a positive sign. You know the particle is at rest when t=0 and t=3, and because the velocity function is continuous, you need only check the sign of v(t) for values on the intervals (0, 3) and (3, 6).

We have, for instance v(1)\approx-0.91 and v(4)\approx0.91>0, which means the particle is moving the positive direction for 3, or the interval (3, 6).

(e) The total distance traveled is obtained by integrating the absolute value of the velocity function over the given interval:

\displaystyle\int_0^6|v(t)|\,\mathrm dt=\int_0^3-v(t)\,\mathrm dt+\int_3^6v(t)\,\mathrm dt

which follows from the definition of absolute value. In particular, if x is negative, then |x|=-x.

The total distance traveled is then 4 ft.

(g) Acceleration is the rate of change of velocity, so a(t) is the derivative of v(t):

a(t)=v'(t)=-\dfrac{\pi^2}9\cos\left(\dfrac{\pi t}3\right)

Compute the acceleration at t=4 seconds:

a(t)=\dfrac{\pi^2}{18}\dfrac{\rm ft}{\mathrm s^2}

(In case you need to know, for part (i), the particle is speeding up when the acceleration is positive. So this is done the same way as part (d).)

6 0
3 years ago
How would I start to solve this? <br> Y=-1/3-1
statuscvo [17]

Answer:

<em>Y = -4/3</em>

Step-by-step explanation:

Subtract 1 from -1/3.

Y = -1/3 - 1

Y = -1/3 - 3/3

Y = -4/3

6 0
2 years ago
Other questions:
  • If AB=4.7 and BD =10.6 cm, what is the length of CD?
    14·1 answer
  • What is the midpoint of the line segment with endpoints (-5.5, -6.1) and (-0.5,9.1)?
    7·1 answer
  • Please help asap 25 pts
    5·1 answer
  • Someone please help!
    14·1 answer
  • Please Help!
    5·1 answer
  • What is decimals -4.8(5.3)
    11·2 answers
  • In April, Phillipa rode
    11·1 answer
  • Enter your answer
    9·1 answer
  • #FleePointsForFlee<br> as you see, #FleePointsForFlee 2
    15·1 answer
  • Fiona wrote the predicted and residual values for a data set using the line of best fit y=3. 71x-8. 85. Which statements are tru
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!