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2 years ago

What are the values of a 1 and r of the geometric series? 1 3 9 27 81.

Mathematics

1 answer:

sp2606 [1]2 years ago

3 0

For the given geometric series the value of the common ratio(r) is 3, while the value of a₁ is 1.

<h3>What is geometric series?</h3>

A series of numbers whose any two consecutive numbers are always in a common ratio of that series.

Given to us

Series, 1 3 9 27 81

To find the value of the common ratio(r), we will simply find the ratio of any two consecutive numbers, therefore,

$r = ratio = \dfrac{3}{1} = 3$

As we can see the common ratio of the given series is 3, therefore, every next number will be thrice the number before.

We need to find the value of a₁ for the given series, and as we know that a₁ is the first number of the series with which the series is starting, therefore,

a₁ = 1

Hence, for the given geometric series the value of the common ratio(r) is 3, while the value of a₁ is 1.

Learn More about Geometric Series:

brainly.com/question/14320920

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salantis [7]

Answer:

$ME=1.96\sqrt{\frac{0.47 (1-0.47)}{800}}=0.0346$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

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Solution to the problem

We assume for this case a confidence level of 95%. In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And if we replace the values obtained we got this:

$ME=1.96\sqrt{\frac{0.47 (1-0.47)}{800}}=0.0346$

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