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
Dafna1 [17]
3 years ago
12

In two or more complete sentences, explain whether the sequence is finite or infinite. Describe the pattern in the sequence if i

t exists, and if possible find the sixth term. 2a, 2a2b, 2a3b2, 2a4b3. . .
Mathematics
2 answers:
Svetlanka [38]3 years ago
8 0
This is infinite since the sequence can go on forever. The sequence increases by 1b every time and the end number is increased 1 every time as well.
<span />
OlgaM077 [116]3 years ago
7 0

Answer:

a). it is an Infinite Sequence.

b). This sequence is Geometric Progression.

c).  6th\,term\,of\,this\,GP\,=\,2a^6b^5                              

Step-by-step explanation:

Given: A Sequence 2a , 2a²b , 2a³b² , 2a^4b^3

To find: a). Given Sequence is finite or infinite

             b). Pattern of the sequence

             c). Sixth term

a). Since, there is no detail about no. of terms of the sequence.

     Therefore, It implies it is an Infinite Sequence.

b). Given 1st term = 2a  ,  2nd term = 2a²b , 3rd term = 2a³b²

    First we find the difference of 1st and 2nd term

    d = 2a²b - 2a  ⇒  d = 2a (ab - 1)

    Now, Difference of 2nd and 3rd term,

    d = 2a³b² - 2a²b = 2a²b (ab - 1)

So, This Sequence is not a Arthematic Progression.

Now, we find the ratio of 2nd term to 1st term,

r\:=\:\frac{2a^2b}{2a}\,=\,ab

Ratio of 3rd term to 2nd term,

r\:=\:\frac{2a^3b^2}{2a^2b}\,=\,ab

Since, the ratio is common.

This sequence is Geometric Progression.

So, Pattern is next term of this sequence has 1 more in  power of a and b

⇒ nth\,term\,of\,this\,GP\,=\,2a^{n}b^{n-1}

c). 6th\,term\,of\,this\,GP\,=\,2a^{6}b^{6-1}

    6th\,term\,of\,this\,GP\,=\,2a^6b^5

Therfore, a). it is an Infinite Sequence.

               b). This sequence is Geometric Progression.

              c).  6th\,term\,of\,this\,GP\,=\,2a^6b^5

                                   

You might be interested in
Complete the point-slope equation of the line through (6,4)and (7,2)
kotykmax [81]
The slope is the change in y over the change in x, so it's (4-2)/(6-7)=2/-1=-2. Point slope form is y<span> – </span>y1<span> = </span>m(x<span> – </span>x1<span>), so we can plug in a point (6,4) to get 
y-6=-2(x-4)</span>
3 0
3 years ago
Read 2 more answers
What is the coefficient of x^4y^4 in the expansion (x+y)^8?
Ivanshal [37]

Answer:

  C.  70

Step-by-step explanation:

In the expansion of (a + b)^n, the k-th term is ...

  nCk·a^(n-k)b^k . . . . . k = 0 to n; nCk = n!/(k!(n-k)!)

Here, we have n=8, k=4, so the term of interest is ...

  8C4·x^4y^4 = (8·7·6·5)/(4·3·2·1)x^4y^4 = 70x^4y^4

The coefficient of the term is 70.

3 0
3 years ago
What is the surface area of the triangular prism (Look at image)
8_murik_8 [283]

Answer:

\Large \boxed{\sf 384 \ m^2}

Step-by-step explanation:

Surface area ⇒ area of 2 triangles + area of 3 rectangles

(8 \times 3 \times 0.5 \times 2)+(20 \times 5 \times 2+20 \times 8)=384

3 0
2 years ago
Read 2 more answers
CONVERT THE PERCENTAGES FRACTION 130%​
Natasha2012 [34]

Answer:

13/10

Step-by-step explanation:

Its 13/10...

please give brainliest

4 0
2 years ago
Read 2 more answers
8x + 3y = 10<br> -2x - 10y =16
Len [333]

Answer:

(2,-2)

x=2

y=-2

7 0
2 years ago
Read 2 more answers
Other questions:
  • mark went to two stores to buy a shirt,pants,and shoes. he wants to know which store has the better deal. ( item:shirts $23.89,p
    13·1 answer
  • What is the standard form for 600,000 80,000 10
    12·1 answer
  • The minute hand of a clock is 4 inches long. how far does the tipof the minute hand move in 20 minnutes?
    5·1 answer
  • 144 what percent of 480?
    6·1 answer
  • A movie club charges a one-time membership fee of $25 which allows members to purchase movies for $7 each. Another club does not
    5·1 answer
  • Plz help me
    5·2 answers
  • (x-4)(x+b)/(x+3)<br><br><br> NEED A ANSWER ASAP
    10·1 answer
  • 1.75 cups of flour makes 12 muffins. If Rob wants to make a batch of 60 muffins, how much flour will he need? please I'm so bad
    10·1 answer
  • Make x the subject of the formula<br> X<br> y = x/a+b
    9·1 answer
  • Solve the attached question .<br>No Spam!<br>Step by step explanation needed!​
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!