Mixing
Arithmetical progression vs. Functions
$begingroup$
I have been studying a lot of Maths recently but I am still in the fundamentals. Although I don't work directly with some topics, I find it very interesting.
Anyways, I was studying arithmetical progression and although I understood the definition as well as the concept, something puzzles me: When do I use arithmetical progression instead of functions? You see, if we take a linear function, it seems a lot like an arithmetical progression, or it is something from my mind? Maybe I lack in experience and I am misunderstanding some concepts.
To illustrate my question lets tackle this problem both using PA and function:
"A guy wants to buy a car whose price is $10.000$. He has saved $4800$ already and he is gonna save $1.200 monthly. How long is it gonna take for him to collect this amount?"
By function:
$f(x) = 1200x + 0$
and we solve for x being $$5200
By PA we simply start at $4800$ and find $N $
As you can see... both ways are possible. So please, when do I use one instead of another?
Thanks in advance
Cheers from Brazil
functions arithmetic-progressions
edited Jan 31 at 17:14
SNEHIL SANYAL
658110
asked Jan 31 at 15:58
Matheus MinguiniMatheus Minguini
175
$endgroup$
add a comment |
$begingroup$
I have been studying a lot of Maths recently but I am still in the fundamentals. Although I don't work directly with some topics, I find it very interesting.
Anyways, I was studying arithmetical progression and although I understood the definition as well as the concept, something puzzles me: When do I use arithmetical progression instead of functions? You see, if we take a linear function, it seems a lot like an arithmetical progression, or it is something from my mind? Maybe I lack in experience and I am misunderstanding some concepts.
To illustrate my question lets tackle this problem both using PA and function:
"A guy wants to buy a car whose price is $10.000$. He has saved $4800$ already and he is gonna save $1.200 monthly. How long is it gonna take for him to collect this amount?"
By function:
$f(x) = 1200x + 0$
and we solve for x being $$5200
By PA we simply start at $4800$ and find $N $
As you can see... both ways are possible. So please, when do I use one instead of another?
Thanks in advance
Cheers from Brazil
functions arithmetic-progressions
edited Jan 31 at 17:14
SNEHIL SANYAL
658110
asked Jan 31 at 15:58
Matheus MinguiniMatheus Minguini
175
$endgroup$
$begingroup$
Arithmetic progressions deal with discrete inputs, namely the integers, whereas functions (typically linear) are continuous. You might find arithmetic progressions used more in computer science, where it might not always be easier to deal with a continuous function.
$endgroup$
– Hyperion
Jan 31 at 16:01
$begingroup$
Also, there are forms you deal with in arithmetic progressions that can't be expressed in continuous functions, namely, recursively defined formulas.
$endgroup$
– Hyperion
Jan 31 at 16:04
$begingroup$
Thanks for your answer...but lemme ask you one thing: Is a PA a Linear function? Or I cant say that?
$endgroup$
– Matheus Minguini
Jan 31 at 16:05
2
$begingroup$
PA is very similar to a linear function, but it is not a linear function. Remember that you are only getting paid every month, not continuously. Since I can't decide to get $$400$ after a third of a month (I can only get my money in $$1200$ chunks every month, this is not continuous, and is most effectively modeled as an arithmetic progression.
$endgroup$
– Hyperion
Jan 31 at 16:09
1
$begingroup$
Nice, now I understand the concept! Thanks for your time and consideration @Hyperion! You are the best ;P
$endgroup$
– Matheus Minguini
Jan 31 at 16:11
add a comment |
$begingroup$
I have been studying a lot of Maths recently but I am still in the fundamentals. Although I don't work directly with some topics, I find it very interesting.
Anyways, I was studying arithmetical progression and although I understood the definition as well as the concept, something puzzles me: When do I use arithmetical progression instead of functions? You see, if we take a linear function, it seems a lot like an arithmetical progression, or it is something from my mind? Maybe I lack in experience and I am misunderstanding some concepts.
To illustrate my question lets tackle this problem both using PA and function:
"A guy wants to buy a car whose price is $10.000$. He has saved $4800$ already and he is gonna save $1.200 monthly. How long is it gonna take for him to collect this amount?"
By function:
$f(x) = 1200x + 0$
and we solve for x being $$5200
By PA we simply start at $4800$ and find $N $
As you can see... both ways are possible. So please, when do I use one instead of another?
Thanks in advance
Cheers from Brazil
functions arithmetic-progressions
edited Jan 31 at 17:14
SNEHIL SANYAL
658110
asked Jan 31 at 15:58
Matheus MinguiniMatheus Minguini
175
$endgroup$
I have been studying a lot of Maths recently but I am still in the fundamentals. Although I don't work directly with some topics, I find it very interesting.
Anyways, I was studying arithmetical progression and although I understood the definition as well as the concept, something puzzles me: When do I use arithmetical progression instead of functions? You see, if we take a linear function, it seems a lot like an arithmetical progression, or it is something from my mind? Maybe I lack in experience and I am misunderstanding some concepts.
To illustrate my question lets tackle this problem both using PA and function:
"A guy wants to buy a car whose price is $10.000$. He has saved $4800$ already and he is gonna save $1.200 monthly. How long is it gonna take for him to collect this amount?"
By function:
$f(x) = 1200x + 0$
and we solve for x being $$5200
By PA we simply start at $4800$ and find $N $
As you can see... both ways are possible. So please, when do I use one instead of another?
Thanks in advance
Cheers from Brazil
functions arithmetic-progressions
functions arithmetic-progressions
edited Jan 31 at 17:14
SNEHIL SANYAL
658110
asked Jan 31 at 15:58
Matheus MinguiniMatheus Minguini
175
edited Jan 31 at 17:14
SNEHIL SANYAL
658110
asked Jan 31 at 15:58
Matheus MinguiniMatheus Minguini
175
edited Jan 31 at 17:14
SNEHIL SANYAL
658110
edited Jan 31 at 17:14
SNEHIL SANYAL
658110
edited Jan 31 at 17:14
SNEHIL SANYAL
658110
658110
asked Jan 31 at 15:58
Matheus MinguiniMatheus Minguini
175
asked Jan 31 at 15:58
Matheus MinguiniMatheus Minguini
175
asked Jan 31 at 15:58
Matheus MinguiniMatheus Minguini
175
175
$begingroup$
Arithmetic progressions deal with discrete inputs, namely the integers, whereas functions (typically linear) are continuous. You might find arithmetic progressions used more in computer science, where it might not always be easier to deal with a continuous function.
$endgroup$
– Hyperion
Jan 31 at 16:01
$begingroup$
Also, there are forms you deal with in arithmetic progressions that can't be expressed in continuous functions, namely, recursively defined formulas.
$endgroup$
– Hyperion
Jan 31 at 16:04
$begingroup$
Thanks for your answer...but lemme ask you one thing: Is a PA a Linear function? Or I cant say that?
$endgroup$
– Matheus Minguini
Jan 31 at 16:05
2
$begingroup$
PA is very similar to a linear function, but it is not a linear function. Remember that you are only getting paid every month, not continuously. Since I can't decide to get $$400$ after a third of a month (I can only get my money in $$1200$ chunks every month, this is not continuous, and is most effectively modeled as an arithmetic progression.
$endgroup$
– Hyperion
Jan 31 at 16:09
1
$begingroup$
Nice, now I understand the concept! Thanks for your time and consideration @Hyperion! You are the best ;P
$endgroup$
– Matheus Minguini
Jan 31 at 16:11
add a comment |
$begingroup$
Arithmetic progressions deal with discrete inputs, namely the integers, whereas functions (typically linear) are continuous. You might find arithmetic progressions used more in computer science, where it might not always be easier to deal with a continuous function.
$endgroup$
– Hyperion
Jan 31 at 16:01
$begingroup$
Also, there are forms you deal with in arithmetic progressions that can't be expressed in continuous functions, namely, recursively defined formulas.
$endgroup$
– Hyperion
Jan 31 at 16:04
$begingroup$
Thanks for your answer...but lemme ask you one thing: Is a PA a Linear function? Or I cant say that?
$endgroup$
– Matheus Minguini
Jan 31 at 16:05
2
$begingroup$
PA is very similar to a linear function, but it is not a linear function. Remember that you are only getting paid every month, not continuously. Since I can't decide to get $$400$ after a third of a month (I can only get my money in $$1200$ chunks every month, this is not continuous, and is most effectively modeled as an arithmetic progression.
$endgroup$
– Hyperion
Jan 31 at 16:09
1
$begingroup$
Nice, now I understand the concept! Thanks for your time and consideration @Hyperion! You are the best ;P
$endgroup$
– Matheus Minguini
Jan 31 at 16:11
$begingroup$
Arithmetic progressions deal with discrete inputs, namely the integers, whereas functions (typically linear) are continuous. You might find arithmetic progressions used more in computer science, where it might not always be easier to deal with a continuous function.
$endgroup$
– Hyperion
Jan 31 at 16:01
$begingroup$
Arithmetic progressions deal with discrete inputs, namely the integers, whereas functions (typically linear) are continuous. You might find arithmetic progressions used more in computer science, where it might not always be easier to deal with a continuous function.
$endgroup$
– Hyperion
Jan 31 at 16:01
$begingroup$
Also, there are forms you deal with in arithmetic progressions that can't be expressed in continuous functions, namely, recursively defined formulas.
$endgroup$
– Hyperion
Jan 31 at 16:04
$begingroup$
Also, there are forms you deal with in arithmetic progressions that can't be expressed in continuous functions, namely, recursively defined formulas.
$endgroup$
– Hyperion
Jan 31 at 16:04
$begingroup$
Thanks for your answer...but lemme ask you one thing: Is a PA a Linear function? Or I cant say that?
$endgroup$
– Matheus Minguini
Jan 31 at 16:05
$begingroup$
Thanks for your answer...but lemme ask you one thing: Is a PA a Linear function? Or I cant say that?
$endgroup$
– Matheus Minguini
Jan 31 at 16:05
2
2
$begingroup$
PA is very similar to a linear function, but it is not a linear function. Remember that you are only getting paid every month, not continuously. Since I can't decide to get $$400$ after a third of a month (I can only get my money in $$1200$ chunks every month, this is not continuous, and is most effectively modeled as an arithmetic progression.
$endgroup$
– Hyperion
Jan 31 at 16:09
$begingroup$
PA is very similar to a linear function, but it is not a linear function. Remember that you are only getting paid every month, not continuously. Since I can't decide to get $$400$ after a third of a month (I can only get my money in $$1200$ chunks every month, this is not continuous, and is most effectively modeled as an arithmetic progression.
$endgroup$
– Hyperion
Jan 31 at 16:09
1
1
$begingroup$
Nice, now I understand the concept! Thanks for your time and consideration @Hyperion! You are the best ;P
$endgroup$
– Matheus Minguini
Jan 31 at 16:11
$begingroup$
Nice, now I understand the concept! Thanks for your time and consideration @Hyperion! You are the best ;P
$endgroup$
– Matheus Minguini
Jan 31 at 16:11
add a comment |
1 Answer
1
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oldest
votes
$begingroup$
Arithmetic progressions, are outputs of a linear function, evaluated at the integer values. This is only a subset of all the values the linear function takes on.
The equation to solve would be 10000=1200x+4800 where x is in months, not dollar dollars. This equation simplifies to 5200=1200x. x is then 4.25 which will be rounded up to the nearest integer to become 5.
answered Feb 18 at 12:28
Roddy MacPheeRoddy MacPhee
724118
$endgroup$
add a comment |
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$begingroup$
Arithmetic progressions, are outputs of a linear function, evaluated at the integer values. This is only a subset of all the values the linear function takes on.
The equation to solve would be 10000=1200x+4800 where x is in months, not dollar dollars. This equation simplifies to 5200=1200x. x is then 4.25 which will be rounded up to the nearest integer to become 5.
answered Feb 18 at 12:28
Roddy MacPheeRoddy MacPhee
724118
$endgroup$
add a comment |
$begingroup$
Arithmetic progressions, are outputs of a linear function, evaluated at the integer values. This is only a subset of all the values the linear function takes on.
The equation to solve would be 10000=1200x+4800 where x is in months, not dollar dollars. This equation simplifies to 5200=1200x. x is then 4.25 which will be rounded up to the nearest integer to become 5.
answered Feb 18 at 12:28
Roddy MacPheeRoddy MacPhee
724118
$endgroup$
add a comment |
$begingroup$
Arithmetic progressions, are outputs of a linear function, evaluated at the integer values. This is only a subset of all the values the linear function takes on.
The equation to solve would be 10000=1200x+4800 where x is in months, not dollar dollars. This equation simplifies to 5200=1200x. x is then 4.25 which will be rounded up to the nearest integer to become 5.
answered Feb 18 at 12:28
Roddy MacPheeRoddy MacPhee
724118
$endgroup$
Arithmetic progressions, are outputs of a linear function, evaluated at the integer values. This is only a subset of all the values the linear function takes on.
The equation to solve would be 10000=1200x+4800 where x is in months, not dollar dollars. This equation simplifies to 5200=1200x. x is then 4.25 which will be rounded up to the nearest integer to become 5.
answered Feb 18 at 12:28
Roddy MacPheeRoddy MacPhee
724118
answered Feb 18 at 12:28
Roddy MacPheeRoddy MacPhee
724118
answered Feb 18 at 12:28
Roddy MacPheeRoddy MacPhee
724118
answered Feb 18 at 12:28
Roddy MacPheeRoddy MacPhee
724118
724118
add a comment |
add a comment |
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$begingroup$
Arithmetic progressions deal with discrete inputs, namely the integers, whereas functions (typically linear) are continuous. You might find arithmetic progressions used more in computer science, where it might not always be easier to deal with a continuous function.
$endgroup$
– Hyperion
Jan 31 at 16:01
$begingroup$
Also, there are forms you deal with in arithmetic progressions that can't be expressed in continuous functions, namely, recursively defined formulas.
$endgroup$
– Hyperion
Jan 31 at 16:04
$begingroup$
Thanks for your answer...but lemme ask you one thing: Is a PA a Linear function? Or I cant say that?
$endgroup$
– Matheus Minguini
Jan 31 at 16:05
2
$begingroup$
PA is very similar to a linear function, but it is not a linear function. Remember that you are only getting paid every month, not continuously. Since I can't decide to get $$400$ after a third of a month (I can only get my money in $$1200$ chunks every month, this is not continuous, and is most effectively modeled as an arithmetic progression.
$endgroup$
– Hyperion
Jan 31 at 16:09
1
$begingroup$
Nice, now I understand the concept! Thanks for your time and consideration @Hyperion! You are the best ;P
$endgroup$
– Matheus Minguini
Jan 31 at 16:11