Mathematics, 03.04.2020 02:26 kalbaugh

Consider the sequence 256, 128 , 64 , 32
find the 12th term of the sequence

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Answer from: ambercable3

The twelfth (12) term of the sequence 256, 128 , 64 , 32...... is 0.125.

Given the following data:

First (1st) term = 256Second term = 128Third term = 64Fourth term = 32

To find the twelfth (12) term of the sequence:

Mathematically, the $n^{th}$ term of a sequence is calculated by using the following formula;

$N_n = \frac{First\; term}{2^{n - 1}}$

Substituting the given parameters into the formula, we have;

$N_{12} = \frac{256}{2^{12 - 1}}\\\\N_{12} = \frac{256}{2^{11}}\\\\N_{12} = \frac{256}{2048}\\\\N_{12} = 0.125$

Therefore, the twelfth (12) term of the sequence is 0.125.

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Answer from: musdaher

The $12^{th}$ of the given sequence is 0.125, if the sequence is 256, 128, 64, 32, ... etc. Which is obtained by the formula of $N_{n}= \frac{F}{ 2^(n-1) }$ .

Step-by-step explanation:

The given is,

The sequence 256, 128, 64, 32,...

Step:1

Formula to calculate the $n^{th}$ therm of the given sequence,

$N_{n}= \frac{F}{2^(n-1) }$ .............................(1)

Where, F - First value

n - Term which is to calculate

From given,

F = 256

n = 12

Equation (1) becomes,

$N_{12}= \frac{256}{2^(12-1) }$

$N_{12}= \frac{256}{2^{11} }$

$= \frac{256}{2048}$

=0.125

$N_{12}$ = 0.125

( or )

Step:1

The given sequence is based on,

To find the next value in sequence the previous value is divided by 2

The $1^{st}$ term is 256

For the $2^{nd}$ term = $\frac{Previous value}{2}$ = $= \frac{256}{2}$ = 128

For the $3^{rd}$ term $= \frac{128}{2}$ = 64

For the $4^{th}$ term $= \frac{64}{2}=32$

For the $5^{th}$ term $= \frac{32}{2}=16$

For the $6^{th}$ term $= \frac{16}{2}=8$

For the $7^{th}$ term $= \frac{8}{2}=4$

For the $8^{th}$ term $= \frac{4 }{2}=2$

For the $9^{th}$ term $= \frac{2}{2}=1$

For the $10^{th}$ term $= \frac{1}{2}=0.5$

For the $11^{th}$ term $= \frac{0.5}{2}=0.25$

For the $12^{th}$ term $= \frac{0.25}{2}=0.125$

The sequence becomes,

256, 128, 64,32,16, 8, 4, 2, 1, 0.5, 0.25, 0.125,..

Result:

The $12^{th}$ of the given sequence is 0.125, if the sequence is 256, 128, 64, 32, ... etc. Which is obtained by the formula of $N_{n}= \frac{F}{ 2^(n-1) }$ .

Answer from: Quest

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Answer from: Quest

we'll this would mean that the dunk tank and the bounce house are the same for 20 hours because the 2 represents that the two activities, and the 20 represents the amount of hours they both are. so with this said, it means that the answer is c. the costs for a dunk tank and bounce house are the same for 20 hours.

c.the costs for a dunk tank and bounce house are the same for 20 hours.

hope this .