Math Formula Needed to Calculate Sequences

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In summary, the conversation discusses finding the number of unique sequences that can be made with a series of numbers from 1 to 16. The formula for this is 16!, which equals 20,922,789,888,000. However, there is no general closed form for factorial and approximations can be made using Stirling's approximation and the error function.
  • #1
Greister
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Hi,

I was wondering if anyone can help me out here...

I have a series of numbers 1 to 16,
What I would like to know is the formula to finding out how many different sequences I can make with them.

For Example:
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16 would be one sequence
2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1 would be another sequence

I thought that if I multiplied 16 by itself, 16 times this would give me the number of sequences I looking for but the answer I got was
18446744073709551616...This can't be right...right?

Anyway thanks for the help if any given.
 
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  • #2
How many different numbers can you put into the first slot?

after you've picked the first number, how many different numbers are left to put into the second slot?

after you've picked the third?
and so on?
 
  • #3
It's like the lotto...I have 16 balls numbered 1-16, there are no duplicate numers.
and there are 16 slots that the balls fall into...all the balls are used filling up the 16 slots.

I need the total number of UNIQUE sequences they can be made into.

The answer to your question above is

Q1 = 16
Q2 = 15
Q3 = 14 ...and so on
 
  • #4
There are:
16 possibilities for the 1st slot,
15 possibilities for the 2nd slot since 1 number is used up,
14 possibilities for the 3rd slot since 2 numbers are used up,
... etc

so that makes 16! = 16*15*14*13* ... *3*2*1 = 20,922,789,888,000 (not 18,446,744,073,709,551,616)

right? :confused: I never liked discrete so I might be wrong. (I'm probably wrong & confused everybody :frown: )
 
Last edited:
  • #5
Sounds right, Its just when I was in school for programming there was an equation to get exactly what I am looking for, which for the life of me I can't find in my past notes. It was some kind of probability equation...

Sorry for my ignorance...from reading the posts on these forums I think I am way out of my league here...hehe
 
  • #6
do not play lotto... (^_^)
 
  • #7
Greister said:
Sounds right, Its just when I was in school for programming there was an equation to get exactly what I am looking for, which for the life of me I can't find in my past notes. It was some kind of probability equation...

Sorry for my ignorance...from reading the posts on these forums I think I am way out of my league here...hehe

There is no general closed form for factorial. It's denoted with an exclamation mark i.e. the number you're looking for can be written as 16!. If you only want approximations, you can look into stirling's approximation and the error function.
 

What is a sequence in math?

A sequence in math is a list of numbers that follow a specific pattern or rule. Each number in the sequence is called a term, and the order of the terms is important.

What is the difference between an arithmetic and geometric sequence?

An arithmetic sequence is a sequence where each term is found by adding a constant number to the previous term. A geometric sequence is a sequence where each term is found by multiplying the previous term by a constant number. In other words, the difference between terms in an arithmetic sequence is constant, while the ratio between terms in a geometric sequence is constant.

How do you find the nth term in a sequence?

To find the nth term in a sequence, you need to first identify the pattern or rule that the sequence follows. Then, you can use that pattern or rule to find the missing term. For example, in an arithmetic sequence, you can use the formula an = a1 + (n - 1)d, where a1 is the first term, d is the common difference, and n is the term number. In a geometric sequence, you can use the formula an = a1 * r^(n-1), where a1 is the first term, r is the common ratio, and n is the term number.

What is the sum of a finite arithmetic or geometric sequence?

The sum of a finite arithmetic sequence can be found using the formula Sn = (n/2)(a1 + an), where n is the number of terms, a1 is the first term, and an is the last term. The sum of a finite geometric sequence can be found using the formula Sn = a1 * (1 - r^n) / (1 - r), where n is the number of terms, a1 is the first term, and r is the common ratio.

How can sequences be applied in real life?

Sequences can be applied in various real-life situations, such as calculating interest rates, population growth, and stock market trends. For example, the compound interest formula is based on a geometric sequence, and predicting future stock prices involves analyzing patterns in past stock market data, which can be represented as a sequence.

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