Please tell us what this question is even asking!...?

Question

Find the first three iterations of each expression:
1) x+3, where x intially equals 12.
2) 3x+2, where x initially equals 4.
3) x squared, minus two, where x initially equals 3.
4) 2(x-3), where x initially equals 1.

Thanks Zarco. You'll get 10 points for your answer, as soon as it will let me pick you (it takes 4 hours).
You saved the day! ;o)

Answer 1

1) f(x)=x+3; f(12)=15; f(f(12))=18; f(f(f(12)))=21
etc.

Answer 2

Well, first of all it's a very poorly set question, but here's what I THINK it means:

A sequence of terms x_1, x_2, ... has general term x_n. [Here, " _i " means " subscript i ".] If for four different sequences, the next term x_(n + 1) is given in terms of x_n by the following expressions, work out x_2, x_3 and x_4 for each of these sequences.

1) x_(n + 1) = x_n + 3, where x_1 = 12.

2) x_(n + 1) = 3 x_n + 2, where x_1 = 4.

3. x_(n + 1) = (x_n)^2 - 2, where x_1 = 3.

4). x_(n + 1) = 2 (x_n - 3), where x_1 = 1.

Now you can probably see what the setter (your teacher?) had in mind. I'll do all three iterations required for the first sequence, just the first two for the second one, and leave the rest to you.

1). x_1 = 12. The "rule" for generating the next one simply says, in effect, "add 3 to each successive term." So:

x_2 = 15; x_3 = 18; x_4 = 21.

2). x_1 = 4. The "generating rule" says "triple the last term and add 2." So:

x_2 = 3*4 + 2 = 14; x_3 = 3*14 + 2 = 44; etc.

Live long and prosper.

P.S. 1. If your teacher really set this question this way, I think that he/she needs a refresher course in expressing mathematics and mathematical questions with care. However, it would probably not be politic to say so!

2. If your teacher wanted to get across the idea of ITERATION as mentioned in the lead up, an ITERATIVE PROCESS should have been defined or specified there. Such a definition or specification would look like this:

x_(n + 1) = f (x_n) for all n > 0, where:

1. f (x_n) = x_n + 3 and x_1 = 12.

2. f(x_n) = 3 x_n + 2 and x_1 = 4. ... etc.

In other words, there is a complete equivalence between setting a "series question" with a term generating rule, or writing it instead in fancy iterative language. But to just throw an expression in x at you and asking you to "iterate" it is, frankly, an abdication of mathematical pedagogy and best practice. (And I say this having had about 48 years of experience.) At the very least the question should SOMEHOW TELL YOU that the result of calculating the value of each f(x) is to be considered as a NEW x for a REPEAT of that process. That is what the CONCEPT of iteration means.

Answer 3

idk sorry