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
Alborosie
3 years ago
6

What are the values of a1 and r of the geometric series? 1 + 3 + 9 + 27 + 81

Mathematics
1 answer:
djyliett [7]3 years ago
8 0
First, notice that the series you wrote is
∑ (-3)(n) for n ∈ [0,5]

There is a general formula for the sum of a basic geometric series that you should know or learn.

Here's a hint: How can you simplify the product of (1-x) and a summation, for n∈ [0,N], of all the n'th powers of x ((1-x)·∑ xn for n∈ [0,N])?

You can see you have to perform a distributive multiplication here, and if you write out the first three or four terms, and the last three or four terms, you should see a lot of cancellation going on. Pay special attention to what happens at n=0, n=N.

(x0+x1+x2+...+xN-2+xN-1+xN)-(x1+x2+...+xN-1+xN+xN+1)

Notice how all the values in between end up cancelling?

You can use your result to find an appropriate formula. In your case, x is 3. N is 5.

If your answer is correct, your formula will work for summing up any number of terms of any geometric series (any value of x and any value N). It is easy to compare your answer using your formula to the answer found manually by actually adding up all the terms.
You might be interested in
25. Solve for x.
Effectus [21]

Answer:

x = 4

Step-by-step explanation:

x * 5 = 20 * 1

x = 4

8 0
3 years ago
Read 2 more answers
600 m equals how many km
anastassius [24]
1000m equals 1km so 600m equals 0.6km.
7 0
3 years ago
Read 2 more answers
A common factor of 2x+10 and 4x+8
OverLord2011 [107]

Answer:

2

Step-by-step explanation:

2(x+5) this is the most you can simplify it

2(2x+4) but you can factor out another 2 so it is 4(x+2)

5 0
3 years ago
98-x2=0 solve this with the quadratic formula
Mars2501 [29]

Answer:

             x∈{-7√2, 7√2}

Step-by-step explanation:

98-x^2=0\\\\-x^2+98=0\\\\a=-1\,,\ \ b=0\,,\ \ c=98\\\\x_1=\dfrac{-0-\sqrt{0^2-4\cdot(-1)\cdot98}}{2\cdot(-1)}=\dfrac{-\sqrt{4\cdot49\cdot2}}{-2}=\dfrac{-2\cdot7\sqrt{2}}{-2}=7\sqrt2\\\\x_2=\dfrac{-0+\sqrt{0^2-4\cdot(-1)\cdot98}}{2\cdot(-1)}=\dfrac{2\cdot7\sqrt{2}}{-2}=-7\sqrt2

7 0
3 years ago
10 PTS!! (5 + 2/8) - (3 7/8)
Artyom0805 [142]
The answer should be 1 3/8
7 0
3 years ago
Read 2 more answers
Other questions:
  • One of your peers claims that boys do better in math classes than girls. Together you run two independent simple random samples
    8·1 answer
  • How many cubes with side lengths of 1/3 cm does it take to fill a rectangular prism with dimensions 1cm, 2 2/3cm and 2/3cm?
    14·1 answer
  • What is the slope of 5x-3y=12
    8·2 answers
  • F=J+Jrt solve following formula for t
    8·1 answer
  • Determine the value of in, in each of the following cases, where n represents all positive integer values.
    6·1 answer
  • X-intercept=4 y-intercept= -2 what is the slope of this line?
    5·1 answer
  • Meg the Stallion placed 8 books on each shelf of a bookcase. If she shelves 32 books. How many shelves are needed?
    7·2 answers
  • Which triangle is a 30°-60-90° triangle?<br><br> 1st Triangle<br> 2nd Triangle<br> 3rd Triangle
    8·1 answer
  • Patterinsin the multiplication table
    7·1 answer
  • What is the 100th term in the list?1017243138
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!