Find the 9th term 1, 3/2, 9/4

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by

2

3

2

3

gives the next term. In other words,

a

n

=

a

1

⋅

r

n

−

1

a

n

=

a

1

⋅

r

n

-

1

.

Geometric Sequence:

r

=

2

3

r

=

2

3

This is the form of a geometric sequence.

a

n

=

a

1

r

n

−

1

a

n

=

a

1

r

n

-

1

Substitute in the values of

a

1

=

1

2

a

1

=

1

2

and

r

=

2

3

r

=

2

3

.

a

n

=

(

1

2

)

⋅

(

2

3

)

n

−

1

a

n

=

(

1

2

)

⋅

(

2

3

)

n

-

1

Apply the product rule to

2

3

2

3

.

a

n

=

1

2

⋅

2

n

−

1

3

n

−

1

a

n

=

1

2

⋅

2

n

-

1

3

n

-

1

Multiply

1

2

1

2

and

2

n

−

1

3

n

−

1

2

n

-

1

3

n

-

1

.

a

n

=

2

n

−

1

2

⋅

3

n

−

1

a

n

=

2

n

-

1

2

⋅

3

n

-

1

Cancel the common factor of

2

n

−

1

2

n

-

1

and

2

2

.

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a

n

=

2

n

−

2

3

n

−

1

a

n

=

2

n

-

2

3

n

-

1

Substitute in the value of

n

n

to find the

n

n

th term.

a

5

=

2

(

5

)

−

2

3

(

5

)

−

1

a

5

=

2

(

5

)

-

2

3

(

5

)

-

1

Simplify the numerator.

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a

5

=

8

3

(

5

)

−

1

a

5

=

8

3

(

5

)

-

1

Simplify the denominator.

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a

5

=

8

81

a

5

=

8

81

Step-by-step explanation:

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

3x + 4y -25 =0 represents the amount of change sianna should recieve