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
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.