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USPshnik [31]
3 years ago
5

What is the 8th term of the sequence? −16, 24, −36, 54, ... −729/8 2187/8 −2187/8 729/8

Mathematics
1 answer:
LUCKY_DIMON [66]3 years ago
8 0

Answer:

The answer is

<h2>\frac{2187}{8}</h2>

Step-by-step explanation:

The sequence above is a geometric sequence

For an nth term in a geometric sequence

A(n) = a ({r})^{n - 1}

where n is the number of terms

r is the common ratio

a is the first term

From the question

a = - 16

To find the common ratio divide the previous term by the next term

That's

r = 24/-16 = -3/2 or -36/24 = - 3/2

Since we are finding the 8th term

n = 8

Substitute the values into the above formula

That's

<h3>A(8) =  - 16 ({ -  \frac{3}{2} })^{8 - 1}</h3><h3>A(8) =  - 16 ({ -  \frac{3}{2} })^{7}</h3><h3>A(8) =  - 16(  - \frac{2187}{128} )</h3><h3 />

We have the final answer as

<h3>A(8) =  \frac{2187}{8}</h3>

Hope this helps you

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Genrish500 [490]

Let 'n' be the number of side of a regular polygon each angle are equal and sum of  each angle equal to (n-2)×180. \\∴For a regular pentagon have five equal side, n=5\\ ∴ sum of each angle = (n-2)×180=3×180 = 540. and ecah angle = 540÷5=108°. Therefore ∠BCG = 108° and ∠ABC =108° \\ Here BE is one of the diagonal of regular pentagon ABCDE. BE divide ∠ABC in 1:2 ratio \\ Therefore ∠ABE : ∠CBE = 36: 72\\∴ ∠GCB + ∠CBE = 108° +72°=180°

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3 years ago
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A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function p(t) = 6t, where t represents t
Neko [114]

Answer:

A)   A[p(t)] = 36πt²

B)   7234.56 square units

Step-by-step explanation:

               

<u>Given functions</u>:

\begin{cases}p(t)=6t \\ A(p)=\pi p^2 \end{cases}

<u>Part A</u>

To find the area of the circle of spilled paint as a function of time, substitute the function p(t) into the given function A(p):

\begin{aligned}A(p) & = \pi p^2\\\\ \implies A[p(t)] & = \pi [p(t)]^2\\& = \pi (6t)^2\\& = \pi 6^2 t^2\\& = 36\pi t^2\end{aligned}

<u>Part B</u>

Given

  • t = 8 minutes
  • π = 3.14

Substitute the given values into the equation for A[p(t)} found in part A:

\begin{aligned}A[p(8)] & = 36\pi t^2\\& = 36 \cdot 3.14 \cdot 8^2\\& = 36 \cdot 3.14 \cdot 64\\& = 113.04 \cdot 64\\& = 7234.56\:\: \sf square\:units\end{aligned}

Therefore, the area of spilled paint after 8 minutes if 7234.56 square units.

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2 years ago
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Answer:

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Step-by-step explanation:

So given sequence is a geometric sequence where terms increase or decrease by a constant common ratio(r)

Formula to find terms in Geometric sequence is " ar^n-1 where a is first term , r is common ratio and n is number of items

In this case , first term (a) is 1 , common ratio(r) is succeeding term/preceding term = 4/1 = 4 and number of items be (n).

Applying "ar^n-1 " we get,

1*4^n-1 which is , 4^n-1

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Answer:

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Step-by-step explanation:

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