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irga5000 [103]
3 years ago
13

A geometric sequence is defined by the equation an = (3)3 − n.

Mathematics
1 answer:
Delvig [45]3 years ago
4 0
PART A

The geometric sequence is defined by the equation

a_{n}=3^{3-n}

To find the first three terms, we put n=1,2,3

When n=1,

a_{1}=3^{3-1}

a_{1}=3^{2}

a_{1}=9
When n=2,

a_{2}=3^{3-2}
a_{2}=3^{1}

a_{2}=3

When n=3

a_{3}=3^{3-3}

a_{3}=3^{0}
a_{1}=1
The first three terms are,

9,3,1

PART B

The common ratio can be found using any two consecutive terms.

The common ratio is given by,
r= \frac{a_{2}}{a_{1}}
r = \frac{3}{9}

r = \frac{1}{3}

PART C

To find
a_{11}

We substitute n=11 into the equation of the geometric sequence.

a_{11} = {3}^{3 - 11}

This implies that,

a_{11} = {3}^{ - 8}

a_{11} = \frac{1}{ {3}^{8} }

a_{11}=\frac{1}{6561}
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(x^2)^2+2(x^2)(9)+9^2

Use Square of Sum: (a+b)^2= a^2+2ab+b^2

(x^2+9)^2

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A child has a box of colored building blocks. He will choose one block without looking. The odds against choosing a blue block a
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Answer:

The answer is "0.2352".

Step-by-step explanation:

Given:

The chance of selecting a odds blue block = \frac{13}{4}

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total number of events are 13+4= 17

Calculating the probability of choosing the blue block  

=\frac{\text{Amount of unfavourable blue block evets} }{\text{Amount of unfavourable blue block evets} } \\\\ = \frac{4}{17} \\\\ =0.2352

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2 years ago
1/4x - 5 = 3/4x - 12
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Answer:

Solve for x

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If the two prisms have equal heights and volumes, what is the length of the x in Prism II?
m_a_m_a [10]

The volume of a prism is given by

V = A_b\cdot h

Where A_b is the base are and h is the height.

So, if two prisms have the same height and the same volume, they must have the same base area.

The first base is an equilateral triangle, which means that the height is given by

h = \dfrac{l\sqrt{3}}{2}

So, the area is

A = 8\cdot\dfrac{8\sqrt{3}}{2} = 32\sqrt{3}

The area of the second base is simply the product of the dimensions, so it is 6.9x

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ANSWER RIGHT FOR BRAINLIEST PLEASE equation of the line that passes through the point (–2, 3) and has a slope of 1/3
morpeh [17]

Answer:

y = \frac{1}{3} x + \frac{11}{3}

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = \frac{1}{3}, thus

y = \frac{1}{3} x + c ← is the partial equation

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3 years ago
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