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romanna [79]
3 years ago
8

Find an equation for the nth term of a geometric sequence where the second and fifth terms are -8 and 512

Mathematics
1 answer:
elixir [45]3 years ago
3 0

Answer:

a_{n} = 2(-4)^{n-1}

Step-by-step explanation:

The n th term of a geometric sequence is

a_{n} = a(r)^{n-1}

where a is the first term and r the common ratio

Given

a_{2} = - 8, then ar = - 8 → (1)

Given

a_{5} = 512, then ar^{4} = 512 → (2)

Divide (2) by (1)

\frac{ar^4}{ar} = \frac{512}{-8}, thus

r³ =- 64 ( take the cube root of both sides )

r = \sqrt[3]{-64} = - 4

Substitute r = - 4 into (1)

a(- 4) = - 8

- 4a = - 8 ( divide both sides by - 4 )

a = 2

Thus

a_{n} = 2(-4)^{n-1}

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A company that explores for oil in the ocean is considering two new sites, A and B. The exploration will take the entire year. T
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Step-by-step explanation:

Hello!

There are two sites A and B,

Be the events A: finding oil in site Awith probability P(A)= 0.6

and B: finding oil in B with probability P(B)= 0.84

A and B are independent (there cannot be found oil of A in B and vice versa)

Remember, two events are independent when the occurrence of one of them doesn't modify the probability of occurrence of the other one in two repetitions of the experiment.

1) Find the probability that oil is found at both sites (round your answer to 2 decimal places)

If there is oil in both sites then event A and B are observed, symbolically:

P(A∩B)

Since both events are independent, the probability of the intersection of both events is equal to the product of each probability so:

P(A∩B)= P(A)*P(B)= 0.6*0.84= 0.504

2) Find the probability that oil is found at only one of the sites (round your answer to 2 decimal places)

In this case, you have two situations in which the statement can occur:

> "finding oil in A" and "not finding oil in B"

-or-

> "not finding oil in A" and "finding oil in B"

Be A' the complementary event of A, i.e. "not finding oil in region A", with probability P(A')= 1 - P(A)= 1 - 0.6= 0.4

And B' the complementary event of B, i.e. "not finding oil in region B", with probability P(B')= 1 - P(B)= 1 - 0.84= 0.16.

You can symbolize these two possible occurrences as:

Remember that "and" indicated intersection between two events, symbolized ∩, and "or" indicates the union between two events, symbolized ∪.

P((A∩B')∪(A'∩B))= P(A∩B') + P(A'∩B)= [P(A)*P(B')]+[P(A')*P(B)]= (0.6*0.16)+(0.4*0.84)= 0.432

I hope it helps!

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