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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.
• 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
• 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
• It's all just different ways of writing a function, so if I said Height (abbrev to H) was a function of time (abbrev to t). Another way of writing that would be H(t). That just tells you H or height is a function of time-which makes sense if something were growing at a constant rate over time. Time is the independent variable and height is the variable that is dependent on the amount of time it takes. It used to confuse me a little too, but any problem with functions will define the rules and the variables of the functions. Another way to think about it is if the function were a chart H(t) would be the y coordinate and t would be the x coordinate value. The y value depends on what the x value is. You can really use any letter combination to define a function just think of the variable in the parenthesis as the x coordinate or the input and the final answer as the output.
• 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.
• At , does a recursive formula have to have n-1, or can I just write 9.7 - 0.1(n)?
(1 vote)
• The function at is the explicit formula (not recursive). You could simplify the explicit formula into your version.

The recursive formula is give in the function h(n). Recursive formulas require that you know the previous term to calculate the next term. So, you would use (n-1).
• does anyone know of a KA vid that properly explains going between the forms a + b(n-1) and a + b(n)?
• It's simpler when calculating. The advantage to using the standard form `9.6 - .01(n-1)` is that you can identify both the first term as well as the common difference without having to calculate them.