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1 year ago

Find the 8th term of the geometric sequence shown below. 6x,18x^4,54x^7 please help

Mathematics

1 answer:

mafiozo [28]1 year ago

7 0

The 8th term of the geometric sequence is 13122x^22

<h3>Explicit form of a geometric sequence</h3>

The explicit form of a geometric sequence is expressed according to the equation;

Tn = ar^n-1

where

r is the common ratio

a is the first term

n is the number of terms

Given the sequence below;

6x,18x^4,54x^7

r = 18x^4/6x

r = 3x^3

a = 6x

n = 8

Substitute to have:

T8 = 6x(3x^3)^8-1

T8 = 6x (3x^3)^7

T8 = 13122x^22

Hence the 8th term of the geometric sequence is 13122x^22

Learn more on geometric sequence here: brainly.com/question/24643676

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elixir [45]

Answer:

The width of billboard is "[x]" and the height of billboard is "[y"]. If total area of billboard is $9000 ft^2$ then $9000=xy$

Step-by-step explanation:

• The total width of billboard is [x]. Therefore the width of printed area will be (x-10) by excluding margin of left and right side.

• The total height of billboard is [y]. Therefore the height of printed area will be [(y-6)] by excluding the margin of top and bottom from the total height.

• To find the printed area of billboard calculations are given below:

$& 9000=xy$

$& y=\frac{9000}{x} \\ & A=(x-10)(y-6) \\ & A=xy-6x-10y+60 \\ & A=x\left( \frac{9000}{x} \right)-6x-10\left( \frac{9000}{x} \right)+60 \\ & A=9060-6x-\frac{9000}{x} \\$

On taking the first order derivative of A

$A'=-6+\left( \frac{90000}{{{x}^{2}}} \right)$

$& \left( \frac{90000}{{{x}^{2}}} \right)-6=0 \\ & 6{{x}^{2}}=90000 \\ & x=\sqrt{15000} \\ & y=\frac{9000}{x}=\frac{90000}{\sqrt{15000}}=10\sqrt{150} \\$