All categories

3 years ago

Find the sixth term of the sequence 1/2, -3/8, 9/32

Mathematics

2 answers:

sukhopar [10]3 years ago

8 0

Answer:

The sixth term is -243/2048 ⇒ answer B

Step-by-step explanation:

* Lets explain the geometric sequence

- There is a constant ratio between each two consecutive numbers

- Ex:

# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)

# 5000 , 1000 , 200 , 40 , …………………………(÷5)

* General term (nth term) of a Geometric sequence:

# U1 = a , U2 = ar , U3 = ar² , U4 = ar³ , U5 = ar^4

# Un = ar^(n-1), where a is the first term , r is the constant ratio

between each two consecutive terms and n is the position of the

number in the sequence

- Ex: U5 = ar^4 , U7 = ar^6 , U10 = ar^9 , U12 = ar^11

- Lets solve the problem

∵ The sequence is 1/2 , -3/8 , 9/32

- Lets find the constant ratio r

∵ The first term is a = 1/2

∵ The second term is U2 = ar

∵ The second term U2 = -3/8

∴ ar = -3/8

∴ 1/2 r = -3/8 ⇒ multiply both sides by 2

∴ r = -3/4

- Lets find the sixth term

∵ a = 1/2 and r = -3/4

∵ n = 6

∴ U6 = ar^5

∴ U6 = 1/2 (-3/4)^5 = 1/2 × -243/1024 = -243/2048

* The sixth term is -243/2048

Umnica [9.8K]3 years ago

8 0

Answer:

B edge

Step-by-step explanation:

You might be interested in

A scientist used 786 milliliters of a liquid for an experiment. How many liters of the liquid did the scientist use for this exp

Charra [1.4K]

Answer:

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

If a hurricane was headed your way, would you evacuate? The headline of a press release issued January 21, 2009 by the survey re

Nikolay [14]

Answer:

The 98% confidence interval for population proportion of people who refuse evacuation is {0.30, 0.33].

Step-by-step explanation:

The sample drawn is of size, n = 5046.

As the sample size is large, i.e. n > 30, according to the Central limit theorem the sampling distribution of sample proportion will be normally distributed with mean $\hat p$ and standard deviation $\sqrt{\frac{\hat p (1-\hat p)}{n} }$ .

The mean is: $\hat p=0.31$

The confidence level (CL) = 98%

The confidence interval for single proportion is:

$CI_{p}=[\hat p-z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} },\ \hat p+z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} }]$

Here $z_{(\alpha /2)}$ = critical value and α = significance level.

Compute the value of α as follows:

$\alpha =1-CL\\=1-0.98\\=0.02$

For α = 0.02 the critical value can be computed from the z table.

Then the value of $z_{(\alpha /2)}$ is ± 2.33.

The 98% confidence interval for population proportion is:

$CI_{p}=[\hat p-z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} },\ \hat p+z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} }]\\=[0.31-2.33\times \sqrt{\frac{0.31\times(1-0.33)}{5046} },\ 0.31+2.33\times \sqrt{\frac{0.31\times(1-0.33)}{5046} } ]\\=[0.31-0.0152,\ 0.31+0.0152]\\=[0.2948,0.3252]\\\approx[0.30,\ 0.33]$

Thus, the 98% confidence interval [0.30, 0.33] implies that there is a 0.98 probability that the population proportion of people who refuse evacuation is between 0.30 and 0.33.

7 0

3 years ago

Answer Mr léonard want to top up his his central heating oil tank

Pachacha [2.7K]

Answer:

step-by-step explanation:

4 0

3 years ago

Help help help help help

wariber [46]

Answer:

Step-by-step explanation:

1) (-6 , 2) ; (3 , -5)

Slope = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$= \frac{-5-2}{3-[-6]}\\\\= \frac{-5-2}{3+6}\\\\= \frac{-7}{9}\\$

m = -7/9 ; (-6 , 2)

y - y₁ = m(x -x₁)

y - 2 = (-7/9)(x - [-6])

$y - 2 = \frac{-7}{9}(x + 6)\\\\y -2 = \frac{-7}{9}x + \frac{-7}{9}*6\\\\y - 2 = \frac{-7}{9}x - \frac{7*2}{3}\\\\ y = \frac{-7}{9}x - \frac{14}{3} + 2\\\\y = \frac{-7}{9}x -\frac{14}{3} + \frac{2*3}{1*3}\\\\y = \frac{-7}{9}x - \frac{14}{3} + \frac{6}{3}\\\\y = \frac{-7}{9}x - \frac{8}{3}$

2) (3 , -4) ; m= 3

$y - y_{1} = m(x - x_{1}$ )

y - [-4] = 3(x - 3)

y + 4 = 3x - 3*3

y + 4 = 3x - 9

y = 3x - 9 - 4

Ans: y = 3x - 13

3) m = 2 ; y-intercept (b) = 3/2

y = mx + b

Ans: y = 2x + (3/2)

4) (-1, 3 ) ; (2 , 0)

Slope = $\frac{0 - 3}{2-[-1]}$

$= \frac{-3}{2+1}\\\\= \frac{-3}{3}\\\\= 1$

m = 1; ( -1 , 3)

y - 3 = 1(x -[-1])

y - 3 = 1(x + 1)

y - 3 = x + 1

y = x + 1 + 3

Ans: y = x + 4

5)(2, 1) ;m = -3

y - 1 = (-3)(x - 2)

y - 1 = -3x + 6

y = -3x + 6 +1

Ans: y = -3x + 7

5 0

4 years ago

Read 2 more answers

A store Is having a sale where movies are 15% off their original price. a movien is on sale for $22.10 what was the orgial price

sergeinik [125]

X= original $

Original $ - % of original $= total $

x - 15%x= $22.10
x- 0.15= 22.10
Combine like terms
0.85x= 22.10
Divide both sides by 0.85
x= $26 original price

Hope this helps! :)

3 0

4 years ago