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Hitman42 [59]
3 years ago
6

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

Mathematics
1 answer:
11Alexandr11 [23.1K]3 years ago
7 0
Easy
recall that
an=a1(r)^(n-1)
so

given 2nd and 5th term

we get
a2 and a5
so
a2=a1(r)^(2-1)=a1(r)^1=a1r
a5=a1(r)^(5-1)=a1(r)^4

also remember that \frac{x^m}{x^n}=x^{m-n}
so
\frac{a_5}{a_2}= \frac{a_1r^4}{a_1r^1}  =r^{4-1}=r^3= \frac{512}{-8}=-64
so r^3=-64
cube root
r=-4
so

a2=a1r=-8
a2=a1(-4)=-8
divide both sides by -4
a1=2

so

equation is
a_n=2(-4)^{n-1}

C isi the answer
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Range represents the y-values from the lowest (furthest down) to the highest (furthest up).

Interval notation: If a value is included <em>(closed dot)</em>, use a bracket [  ]

                      If a value is NOT included <em>(open dot)</em>, use a parenthesis (  )

                     Note that ± ∞ is never included.

1. Domain: smallest x-value is -4 (included). biggest x-value is 3 (included)

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2. Domain: smallest x-value is -∞ (←). biggest x-value is 2 (included)

  Range: lowest y-value is 2 (included). highest y-value is ∞ (↑)

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3. Domain: smallest x-value is -∞ (←). biggest x-value is ∞ (→)

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4. Domain: smallest x-value is -∞ (←). biggest x-value is ∞ (→)

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5. Domain: smallest x-value is -∞ (←). biggest x-value is ∞ (→)

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Answer: y = (-4/5)x + 8

Solution

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y = mx + b

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Shown in the graph

<h2>Explanation:</h2>

Using graph tools we can graph the function:

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Let \ c \ be \ a \ positive \ real \ number. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:

\bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ h(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ h(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ right \ \mathbf{right}: \\ h(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ left \ \mathbf{left}: \\ h(x)=f(x+c)

Therefore, If we shift the red graph 9 units to the right and 1 down, our new function (let's call it h(x)) will be:

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This graph is the blue graph below. Let's verify the transformation taking the vertex of the red graph:

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By translating the 9 units to the right and 1 down the vertex is also translated by the same rule, so:

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<h2>Learn more:</h2>

Cubic function: brainly.com/question/13773618#

#LearnWithBrainly

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