All categories

4 years ago

Use the formula to evaluate the series -3 + 6 - 12 +24 - ...-az.

Mathematics

1 answer:

aleksklad [387]4 years ago

3 0

Answer:

Your sum = $(-2)^{z}$ - 1

S = ( (-2)^n - 1), If you let n = z, then S = (-2)^z - 1

Step-by-step explanation:

I can use a formula to find the sum of the first n terms.

we have -3, 6, -12, 24, ... etc.

common ratio = r = -2

first term = -3

a_1 = -3

Then: a_n = a_1 * r ^(n -1)

a_n = (-3) * (-2)^(n - 1) is the general formula for the nth term

Sum of first n terms = S = a_1 * (r^n - 1) / (r - 1)

so...

S = (-3) * ((-2)^n - 1 )/ (-2 - 1)

which simplifies to

S = (-3) *((-2)^n - 1) / (-3)

S = ( (-2)^n - 1)

If you let n = z, then S = (-2)^z - 1

You might be interested in

Who is faster?

Kay [80]

Kendra is going faster. You could convert Kendra's measurement to feet per second by doing to following:

0.25 mi/1 min x 5280 ft/1 mi x 1 min/60 sec

Which equals:

(0.25)(5280)ft/60 sec

Simplify, and Kendra's speed is 22 feet per second.

mi= mile(s)
min= minute(s)
ft= feet
sec= second(s)

6 0

3 years ago

Write the product (4 + i)(4 − i) in the form a + bi. A. 16 − i B. 16 − i2 C. 17 D. 8

bonufazy [111]

Answer:

A.16–i is correct.

Step-by-step explanation:

(4+i)(4–i). [(a+b)(a–b)=(a²–b²)]

(4²–i²)=16–i

I hope this answer is correct so please vote my answer

3 0

4 years ago

Micheal signed a 5-year contract for a new job. His starting salary is $67K per year, and the salary increases 3% each year if a

Tcecarenko [31]

Answer: 77050

Step-by-step explanation: each year +3% meaning in 5 years should be 15% already. 15/100 times x/67000. use butterfly method.

4 0

3 years ago

A 20 foot ladder leaning against a wall is used to reach a window that is 17 feet above the ground. How far from the wall is the

Liono4ka [1.6K]

Answer:

The wall is 10.5 foot far from the bottom of the ladder.

Step-by-step explanation:

Given:

Height of the ladder leaning against wall (Hypotenuse) = 20 foot.

Height from where the window is above from the ground (Leg1) = 17 feet.

To find the distance of the bottom of the ladder far from the wall (Leg2) = ?

Now, by using the pythagorean theorem:

$Hypotenuse^{2} = (Leg1)^{2} + (Leg2)^{2}$

$20^{2} =17^{2}+(Leg2) ^{2}$

$400=289+(Leg2)^{2}$

$400-289=(Leg2)^{2}$

$111=(Leg2)^{2}$

by squaring both sides

$Leg2=10.535$

10.535 foot rounded nearest tenth is 10.5 foot.

Therefore, the wall is 10.5 foot far from the bottom of the ladder.

6 0

3 years ago

If a sample of 362 customers is taken from a population of 5530 customers,

inysia [295]

Using concepts of sample and population, it is found that the sample variance is representative of 362 and 5530 customers ages, option D.

------------------------

In sampling, the information is taken from a sample, and is used to estimate it for the whole population.

In this problem, we have a sample of 362 and a population of 5530 customers.
The sample variance $s^2$ is calculated from the sample, and used as an estimate for the population variance. Thus, it can be said that it represents both 362 and 5530 customers, and the correct option is D.

A similar problem is given at brainly.com/question/4086221

6 0

2 years ago