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
romanna [79]
3 years ago
12

Find the sum of the geometric sequence. (1 point) 1, 1/2, 1/4, 1/8, 1/16

Mathematics
2 answers:
ASHA 777 [7]3 years ago
8 0
Sn  = a1 * (1 - r^n)
                 ----------
                   1 - r

n = 5   so answer  =

   1 * (1 -  (1/2)^5
        ---------------  =       31/16  
               1 - 1/2
           
wariber [46]3 years ago
8 0
That finite sequence we can just add up, using 16 as a common denominator

1 + 1/2 + 1/4 + 1/8+1/16 = 16/16 + 8/16 + 4/16+2/16+1/16 = (16+8+4+2+1)/16=31/16

They probably want you to use the formula

S_n = \sum_{k=0}^{n-1} r^k = \dfrac{1 - r^n}{1-r}

That's the special case of a geometric series where the first term is one.  If it's not we multiply the answer by the first term.

In our example, r=1/2 and n=5, meaning five terms.

S_5 = \dfrac{ 1- (1/2)^5}{1- (1/2)} = \dfrac{1-1/32}{1/2}=\dfrac{31/32}{1/2}=\dfrac{31}{15}

Same answer, math works!

If the question was asking about the infinite geometric series, that's just a little bigger:

S = \dfrac{1}{1-r} = \dfrac{1}{1 - \frac 1 2} = 2


You might be interested in
Can someone help me please?
Gwar [14]

Answer:

10.5 cm^2

Step-by-step explanation:

Area of a triangle = 1/2(L x H)

Reading from the diagram

length = 7 cm

height = 3 cm

therefore

Area of the triangle = 1/2( 7×3)

Area = 10.5 cm^2

4 0
3 years ago
Is the function even or odd?
sweet [91]

Answer:

f(\theta)=\cos(\theta) is an even function.

Step-by-step explanation:

Recall when it means when a function is even or odd. An even function has the following property:

f(-x)=f(x)

And an odd function has the following property:

f(-x)=-f(x)

So, let's test some values for cos(x).

Let's use π/3:

f(\pi/3)=\cos(\pi/3)

From the unit circle, was can see that this is 1/2 (refer to the x-coordinate).

Now, let's find -π/3. This is the same as 5π/3. Thus:

f(-\pi/3)=\cos(-\pi/3)

And again from the unit circle, we can see that this is 1/2.

Therefore, despite the negative, the function outputs the same value.

Cosine is an even function.

Notes:

Cosine is an even function and sine is an odd function. It's helpful to remember these as they can help you solve some trig problems!

6 0
3 years ago
Answer fast please .
MArishka [77]
I think it's D. The area of A is k2 times the area of rectangle B
8 0
3 years ago
if 20 students ride on your bus and two fifth of them pack there lunches how many of them didnt pack there lunch
Vadim26 [7]
Your Answer Is...

12.

(If you need an explanation, comment below.)

Glad I Could Help, And Good Luck!

~AnonymousGiantsFan~
5 0
3 years ago
BRANILIEST ANSWER GETS ALOT OF POINTS I NEED HELP PLZZ
yulyashka [42]
For this problem, I'd use cross-multiplication.

9/12 = x/8.

When cross multiplying, multiply 12*x and 9*8. This leads to a new equation:

12x = 72.

Then you solve as an algebra problem.

*Divide 12 on both sides*

x = 6.
6 0
4 years ago
Other questions:
  • Sammy is conducting a science experiment were he has to mix 8. 25 ounces and 430 ounces of lemon juice. How many ounces will he
    6·1 answer
  • Holiday Company is a seasonal business. It earned twice as much in the fourth quarter as it did in each of the other quarters. W
    13·1 answer
  • What is the answer to this question can you please answer right
    13·1 answer
  • What is the equation of the line that passes through the points (−2, 1) and (1, 10)?
    11·1 answer
  • Pls help a girl out .......
    8·1 answer
  • What translation is made from f(x) = f(x) + 6?
    13·2 answers
  • Here is Triangle A. Lin created a scaled copy of Triangle A with an area of 72 square units. C. What is the length of bottom sid
    7·1 answer
  • Jynessa wants to order these fractions 4/9, 2/3, 1/6, -2 1/2 what should she use as her common denominator?
    11·1 answer
  • what is the difference in height between 30 m up a cliff and 87 m up a cliff? What is the distance between these positions?
    7·2 answers
  • help help help help help help help help help help help help help help help help help help help help help help help help help hel
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!