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

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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

goog may be able to you find that answer

Which table represents a linear function?

Answer from: Quest

.there can be infinite values of m and n that can satisfy the above equation. for each value of m of m or n. there maybe infinite sets of solution for the above

step-by-step explanation:

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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...