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3 years ago

What are the possible values of the missing term in the geometric sequence? 4, _, 9, ...

Mathematics

1 answer:

pashok25 [27]3 years ago

4 0

<h3>Two possible answers: 6 or -6</h3>

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Explanation:

r = common ratio

To get any term in a geometric sequence, we multiply the previous term by r.

So that means 4r is the second term, since 4 is the first term.

The third term is (4r)*r = 4r^2, which is equal to 9 as given to us.

4r^2 = 9

4r^2 - 9 = 0

(2r)^2 - (3)^2 = 0

(2r - 3)(2r + 3) = 0 ... difference of squares rule

2r-3 = 0 or 2r+3 = 0

2r = 3 or 2r = -3

r = 3/2 or r = -3/2

r = 1.5 or r = -1.5

We can use each r value to find the possible second term

S = 4r = 4*(1.5) = 6

S = 4r = 4*(-1.5) = -6

The second term is either 6 or -6.

We could have this sequence: 4, 6, 9, ...

Or we could have this sequence: 4, -6, 9, ...

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Answer:

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b) We have that the significance is given by $\alpha =0.05$ , $\alpha/2 =0.025$ and we know that we have a two tailed test.

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Step-by-step explanation:

Part a

We have that the significance is given by $\alpha =0.01$ and we know that we have a right tailed test.

"=NORM.INV(1-0.01,0,1)"

And we got for this case $z_{crit}=2.33$

So then the rejection region would be $z>2.33$

Part b

We have that the significance is given by $\alpha =0.05$ , $\alpha/2 =0.025$ and we know that we have a two tailed test.

"=NORM.INV(1-0.025,0,1)"

And we got for this case $z_{crit}=\pm 1.96$

So then the rejection region would be $z>1.96 \cup z$

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