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3 years ago

Find the first six terms of the sequence. a1 = -1, an = 2 • an-1

Mathematics

2 answers:

kompoz [17]3 years ago

7 0

Answer:

The first six terms of the sequence are: -1, -2, -4, -8, -16 and -32

Step-by-step explanation:

The sequence is:

$a_1=-1\\a_n=2*a_{n-1}$

So, for finding the first six terms of the sequence, we need to replace n by the numbers 1 to 6 and we get:

$a_1=-1\\a_2=2*a_{2-1} =2*a_1\\a_3=2*a_{3-1} =2*a_2\\a_4=2*a_{4-1} =2*a_3\\a_5=2*a_{5-1} =2*a_4\\a_6=2*a_{6-1} =2*a_5\\$

That means that the term n is 2 times the last term. Then, replacing the values of $a_1, a_2, a_3, a_4$ and $a_5$ , we get:

$a_1=-1\\a_2=2*(-1)=-2\\a_3=2*(-2)=-4\\a_4=2*(-4)=-8\\a_5=2*(-8)=-16\\a_6=2*(-16)=-32\\$

So, The first six terms of the sequence are: -1, -2, -4, -8, -16 and -32

allochka39001 [22]3 years ago

3 0

The prompt says that the value at n is equal to 2 times the previous value.
-1, -2, -4, -8, -16, -32

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Solving system of equations by substitution

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3x+6x-20=16
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4 years ago

It is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get less than seven hours of sleep per nig

Kitty [74]

Answer: No , at 0.05 level of significance , we have sufficient evidence to reject the claim that LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average.

Step-by-step explanation:

Let $\mu$ denotes the average hours of sleep per night.

As per given , we have

$H_0:\mu=7\\H_a:\mu$

, since $H_a$ is left-tailed and population standard deviation is unknown, so the test is a left-tailed t -test.

Also , it is given that ,

Sample size : n= 22

Sample mean : $\overline{x}=7.24$

Sample standard deviation : s= 1.93

Test statistic : $t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}$

i.e. $t=\dfrac{7.24-7}{\dfrac{1.93}{\sqrt{22}}}\approx0.58$

For significance level $\alpha=0.05$ and degree of freedom 21 (df=n-1),

Critical t-value for left-tailed test= $t_{\alpha, df}=t_{0.05,21}=- 1.7207$

Decision : Since the test statistic value (0.58) > critical value 1.7207, it means we are failed to reject the null hypothesis .

[Note : When $|t_{cal}|>|t_{cri}|$ , then we accept the null hypothesis.]

Conclusion: We have sufficient evidence to reject the claim that LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average.

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3 years ago

There are 4 consecutive integers that add up to 154. what is the least of these integers?

ElenaW [278]

I guesstimated and checked my answer to get 37.
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3 years ago

Read 2 more answers

Classify the following random variables as discrete or continuous:X: the number of automobile accidents per year in Virginia. Y

Elena-2011 [213]

Answer:

X: discrete

Y: continuous

M: continuous

N: discrete

P: discrete

Q: continuous

Step-by-step explanation:

First, we have to know the difference between discrete and continuous variables:

Discrete variables are those that represent things that are counted, 3 red cars, 2 chickens, etc.. They take positive integer values, {0, 1, 2, ..., n}, being [0, n] the interval from which the variable takes values, that means, there is a finite number of possible values.
Continuous variables are those that represent things that are measured, 3.56 km of railway laid, 5.77 l of paint used. They take positive real values, that means that in the interval used for the variable there are infinite possible values.

Now, we classify each variable:

The number of automobile accidents per year in Virginia (X) is a discrete variable, as there can't be half an accident, one counts how many accidents are per year to know X.
The length of time to play 18 holes of golf (Y) is a continuous variable, as it can take 2 hours, or 2.5 hours, or 2 hours, 30 minutes, 2 seconds, one measures how long it took to play 18 holes to know Y.
The amount of milk produced yearly by a particular cow (M) is a continuous variable, as one measures how much milk was produced to know M.
The number of eggs laid each month by a hen (N) is a discrete variable, as one counts how much eggs were laid to know N.
The number of building permits issued each month in a certain city (P) is a discrete variable, as one counts how many permits were issued to know P.
The weight of grain produced per acre (Q) is a continuous variable, as one measures the weight per acre to know Q.

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WARRIOR [948]

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