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# Converting recursive & explicit forms of arithmetic sequences

Sal is given an arithmetic sequence in explicit form and he converts it to recursive form. Then he does so the other way around!

## Want to join the conversation?

• So an arithmetic sequence has a constant rate right
• Right, because the common difference is always constant in arithmetic sequences.
• Is arithmetic sequence basically a linear function with the domain of positive integers?
Are there other differences?
• Late comment. The others are correct. To expand, if you graphed your sequence, you would get what looks like dots that can be connected by a line (just like the functions in the previous playlist). As we only look at positive integers, the line wouldn't actually be drawn.
• what's the meaning of "h" and "g" f is function and n stand for number of times (i guess) but what about the first two
• Each function has a name which is {h, g, f,...}, an input like n, an output {h(n), g(n), f(n),...}, and a relationship that connects the input and the output like the formula in this video:
`h(n) = -31 - 7(n-1)`
Hope this helps!
• so can the recursive formula be stated in 2 ways or is there a preferred version.
g1 = x, gn = g(n-1) + y
or g(n) = x if n = 1
= g(n-1) + y if n > 1
• the recursive formula can be stated in two ways/ forms. however, there is the preferred version, which is g(n)= g(n-1) +y. technically you can change it into g(n)= y+ g(n-1). it's just easier to see/ visualize the function in the first format rather the second one.
• at doesn't he mean subtract seven not negative seven
• Yeah, it seems he corrected this in the video annotations after the fact
• Why would you even want to do this? How is this used in real life and why do you need to change formulas?
• Q1: Sequences come in handy in higher maths when you begin calculus. In the "real world", sequences are used in many areas, including home loans and engineering (to name a few).

Q2: The changing of the formulas is shown for your knowledge. Since there are 2 formulas available, it's good to know how to get one from the other. Also, students often prefer one over the other. Given a formula, those students can convert it into their preferred one.
• In which part of daily life, this type of theory is used?
• Well, most likely you won't use this however algebra, and other difficult math are used to show how fast and capable you are of understanding hard concepts. So it you make A+'s in trigonometry or something like that the company you are trying to apply for will think "Ok, he can understand hard things and do well let's hire him!" Does that make any sense?
• He never explains what an explicit formula is. Or how to formate one.