Mathematics, 30.07.2019 02:30 dondre54

What would be the next number in pattern 1/324, 1/108, 1/36, 1/12 answers are 1/3, 1/5, 1/4, 1

Answers: 2

Show answers

Answers

The answer would be 1/4. Each number is increasing by a multiple of 3. 1/324 x 3 = 1/1081/108 x 3 = 1/36...etc. So 1/12 x 3 = 1/4. Another way to look at it is to ignore the 1/ at the front since that stay consistent and only look at the 2nd part. In that case, each number is decreasing by 1/3.

Answer from: thomas0022

The next number in pattern 1/324, 1/108, 1/36, 1/12 would be 1/4

Further explanation

Firstly , let us learn about types of sequence in mathematics.

Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.

$\boxed{T_n = a + (n-1)d}$

$\boxed{S_n = \frac{1}{2}n ( 2a + (n-1)d )}$

Tn = n-th term of the sequence

Sn = sum of the first n numbers of the sequence

a = the initial term of the sequence

d = common difference between adjacent numbers

Geometric Progression is a sequence of numbers in which each of adjacent numbers have a constant ration.

$\boxed{T_n = a ~ r^{n-1}}$

$\boxed{S_n = \frac{a( 1 - r^n ) }{1 - r}}$

Tn = n-th term of the sequence

Sn = sum of the first n numbers of the sequence

a = the initial term of the sequence

r = common ratio between adjacent numbers

Let us now tackle the problem!

Given:

This problem is about Geometric Sequence. Let's see why.

$\frac{1}{324} , \frac{1}{108} , \frac{1}{36} , \frac{1}{12} , . . .$

T₁ = $\frac{1}{324}$

T₂ = $\frac{1}{108}$

T₃ = $\frac{1}{36}$

T₄ = $\frac{1}{12}$

$\large {\boxed {\frac{T_2}{T_1} = \frac{T_3}{T_2} = \frac{T_4}{T_3} = r = 3} }$

From the above results it can be concluded that this is Geometric Sequence.

The next number will be the fifth term and can be calculated as following.

$T_n = a ~ r^{n-1}$

$T_5 = \frac{1}{324} \times 3^{5 - 1}$

$T_5 = \frac{1}{324} \times 3^4$

$T_5 = \frac{1}{324} \times 81$

$\large {\boxed {T_5 = \frac{1}{4} } }$

Learn moreGeometric Series : Arithmetic Progression : Geometric Sequence : Answer details

Grade: Middle School

Subject: Mathematics

Chapter: Arithmetic and Geometric Series

Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term

What would be the next number in pattern 1/324, 1/108, 1/36, 1/12 answers are 1/3, 1/5, 1/4, 1

Answer from: Quest

step-by-step explanation:

a. since the profit made in 2012 is equal to the profit made in 2014, the profit is symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since 2010 0 1 2 3 4 5

profits made in 1000's 39 84 111 120 111 84

we find that profit gradually increases form 2010 to 2013 upto 120, then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a. since the profit made in 2012 is equal to the profit made in 2014, the profit is symmetric about the line y = 120,000.

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 16:00, allieballey0727

Graph the equation by plotting point x=2

Answers: 1

continue

Mathematics, 21.06.2019 16:50, lunamoon1

The rate of decay of a radioactive substance depends upon the amount present initially. the mass y (mg) of the radioactive substance cobalt-60 present in a sample at time t (years) is represented by the exponential equation y=50e −0.1315 t . answer the following questions in complete sentences. 1. how does the exponential equation above compare to the equation for simple interest that is compounded continuously? explain the similarities. 2. what is the initial amount of cobalt-60 in the sample? 2. how much cobalt-60 is left after 8.4 years? show your work. 3. what would be the y-intercept of the graph? what does it represent? 4. after how many years will the amount of cobalt-60 left be 6.25 mg? explain what happens to the cobalt-60 after 50 years? 5. discuss some “real-world” examples and uses of cobalt-60

Answers: 1

continue

Mathematics, 21.06.2019 21:30, shymitch32

Create a graph for the demand for starfish using the following data table: quantity/price of starfish quantity (x axis) of starfish in dozens price (y axis) of starfish per dozen 0 8 2 6 3 5 5 2 7 1 9 0 is the relationship between the price of starfish and the quantity demanded inverse or direct? why? how many dozens of starfish are demanded at a price of five? calculate the slope of the line between the prices of 6 (quantity of 2) and 1 (quantity of 7) per dozen. describe the line when there is a direct relationship between price and quantity.

Answers: 3

continue

Mathematics, 21.06.2019 22:00, mileto1798

Write a description of each inequality. 1. -5a + 3 > 1 2. 27 - 2b < -6 (this < has a _ under it) 3. 1/2 (c + 1) > 5 (this > has a _ under it)

Answers: 3

continue

You know the right answer?

What would be the next number in pattern 1/324, 1/108, 1/36, 1/12 answers are 1/3, 1/5, 1/4, 1...