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3 years ago

What is the sum of the geometric sequence -3,18,-108,.. if there are 7 terms?

Mathematics

1 answer:

andreev551 [17]3 years ago

5 0

Answer:

$S_{7}$ = - 119973

Step-by-step explanation:

The sum to n terms of a geometric sequence is

$S_{n}$ = $\frac{a(r^n-1)}{r-1}$

where a is the first term and r the common ratio

Here a = - 3 and r = 18 ÷ - 3 = - 6 , thus

$S_{7}$ = $\frac{-3(-279936-1)}{-6-1}$

= $\frac{-3(-279937)}{-7}$

= $\frac{839811}{-7}$

= - 119973

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3 years ago

Can someone solve this for me please.

nika2105 [10]

Answer:

The value of PR is 21 ft.

Step-by-step explanation:

We know that:

3(PQ + QT + TP) = PR + RS + SP
PQ = 7 ft.
QT = 4 ft
RS = 12 ft.

Work:

3(PQ + QT + TP) = PR + RS + SP
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2 years ago

Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its average number of unoc

Bingel [31]

Answer:

We need a sample size of at least 719

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.025 = 0.975$ , so $z = 1.96$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

How large a sample size is required to vary population mean within 0.30 seat of the sample mean with 95% confidence interval?

This is at least n, in which n is found when $M = 0.3, \sigma = 4.103$ . So

$M = z*\frac{\sigma}{\sqrt{n}}$

$0.3 = 1.96*\frac{4.103}{\sqrt{n}}$

$0.3\sqrt{n} = 1.96*4.103$

$\sqrt{n} = \frac{1.96*4.103}{0.3}$

$(\sqrt{n})^{2} = (\frac{1.96*4.103}{0.3})^{2}$

$n = 718.57$

Rouding up

We need a sample size of at least 719

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3 years ago