All categories

3 years ago

What is the sum of the first 7 terms of the geometric series: -8 + (-4) + (-2) + 1 + 1/2+...

1 answer:

s2008m [1.1K]3 years ago

4 0

$a_1=-8;\ a_2=-4;\ r=a_2:a_1\to r=-4:(-8)=\dfrac{1}{2};\ n=7\\\\S_n=\dfrac{a_1(1-r^n)}{1-r}\\\\subtitute:\\\\S_7=\dfrac{-8\left[1-\left(\dfrac{1}{2}\right)^7\right]}{1-\dfrac{1}{2}}=\dfrac{-8\left(1-\dfrac{1}{128}\right)}{\dfrac{1}{2}}\\\\=\dfrac{-8\cdot\dfrac{127}{128}}{\dfrac{1}{2}}=-\dfrac{127}{16}\cdot\dfrac{2}{1}=-\dfrac{127}{8}=-15\dfrac{7}{8}$

You might be interested in

A piece of string 25 and 1/2 inches long will be cut into 3/4 inch pieces how many pieces will there be

olga2289 [7]

you would have 9.375 pieces or 75/8 pieces, depends on how you look at it

6 0

3 years ago

Determine the radius, to the nearest inch, of a large can of tuna fish that has a volume of 66 cubic

Mnenie [13.5K]

The radius of can is 2.524 inches

Solution:

Given that large can of tuna fish that has a volume of 66 cubic inches and a height of 3.3 inches

To find: Radius

Given a large can of tuna fish, we know that can is generally of cylinder shape, we can use the volume of cylinder formula,

The volume of cylinder is given as:

$\text{ volume of cylinder}= \pi r^{2} h$$

Where,

"r" is the radius of cylinder

"h" is the height of cylinder

$\pi$ is a constant equal to 3.14

Substituting the given values in above formula,

$66 = 3.14 \times r^2 \times 3.3\\\\66 = r^2 \times 10.362\\\\r^2 = \frac{66}{10.362}\\\\r^2 = 6.369\\\\r = 2.524$

Thus the radius of can is 2.524 inches

4 0

3 years ago

Ruth decides to use the method of proportions and similar triangles to find the height of a tree. She measures the length of the

musickatia [10]

Answer:

c. 24 ft

Step-by-step explanation:

if the 12 inch ruler casts a 6 inch shadow (shadow has half size) then a tree with 12 feet long shadow will have a height of 24 feet

5 0

3 years ago

Please help and thank you

yulyashka [42]

Answer:

D) 3

Step-by-step explanation:

It is halfway the length of Y and W. 6-3= 3

Note:

Pls notify me if my answer is incorrect for the other users that will see this response. Thank you.

-kiniwih426

5 0

3 years ago

Read 2 more answers

Which terms could be used as the first term of the expression below to create a polynomial written in standard form? Select five

Alina [70]

Answer:

3r⁴s⁵

- r⁴s⁶

- 6rs⁵

Step-by-step explanation:

1) The expression given is:

+ 8r²s⁴ – 3r³s³

2) The choices given are:

s⁵

3r⁴s⁵

- r⁴s⁶

- 6rs⁵

1) A polynomial written in standard form has the terms ordered in decreasing order.

For example, 4x⁵ + 8x⁴ + 3x² + 27

2) The given polynomial has degree 6: + 8r²s⁴ – 3r³s³, and it can be ordered respect any of the two variables either r or s.

3) Adding a new term as first term needs to have degree equal or greater than 6.

So, the candidates from the list are: 3r⁴s⁵, - r⁴s⁶,- 6rs⁵

4) If you use 3r⁴s⁵, the polynomial in standard form would be:

3r⁴s⁵ – 3r³s³ + 8r²s⁴ (as you see the degree of r is decreasing from left to right).

5) If you use - r⁴s⁶, the polynomial in standard form would be:

- r⁴s⁶ – 3r³s³ + 8r²s⁴ (as you see, the degree of r decreases from left to right)

6) If you use - 6rs⁵, the polynomial in standard form would be

- 6 rs⁵– 3r³s³ + 8r²s⁴ (as you see the degree of s is decreasing from left to right).

7) You cannot use s⁵ as first term because its degree is less than 6.

3 0

3 years ago

Read 2 more answers