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Temka [501]
2 years ago
15

Write the explicit formula for this geometric sequence.

Mathematics
1 answer:
Naily [24]2 years ago
7 0

The explicit formula for this  geometric sequence 81, 27, 9, 3, … is aₙ = 81(1/3)ⁿ⁻¹. It has common ratio of 1/3 and first term of 81.

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more variables and numbers.

A geometric sequence is in the form aₙ = ar⁽ⁿ⁻¹⁾, where a is the first term and r is the common ratio.

The geometric sequence 81, 27, 9, 3, … has common ratio:

r = 27/81 = 1/3

The explicit formula for this  geometric sequence 81, 27, 9, 3, … is aₙ = 81(1/3)ⁿ⁻¹. It has common ratio of 1/3 and first term of 81.

Find out more on equation at: brainly.com/question/2972832

#SPJ1

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3 years ago
An arhitect wants to draw a rectangle with a diagonal of 20 inches. The length of the rectangle is to be 8 inches more than twic
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The diagonal of a rectangle = sqrt(w^2 + l^2)

w = width

l = length

In this problem,

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w = x

l = 2x + 8

Let's plug our numbers into the formula above.

20in = sqrt((x)^2 + (2x + 8)^2)

Let's simplify the inside of the sqrt

20 in = sqrt(5x^2 + 32x + 64)

Now, let's square both sides.

400 = 5x^2 + 32x + 64

Subtract 400 from both sides.

0 = 5x^2 + 32x - 336

Factor

0 = (5x - 28)(x + 12)

Set both terms equal to zero and solve.

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Subtract 12 from both sides.

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Add 28 to both sides.

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Divide both sides by 5

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The width cant be a negative number so now we know that the only real solution is 28/5

Let's plug 28/5 into our length equation.

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In conclusion,

Length = 96/5 inches

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