Monday, April 30, 2007

Prompt Answer

What questions do you have on this topic?
I only have one question actually, when we use the first form of the explicit formula. Y=mx+b to find the nth term, does it wrok for arithmetic, geometric, complex or all kind of sequences.

What mistakes are you most likely to make?
The most common mistakes I make, are never big mistakes. I tend to miss very small things, like decimals, negatives or small algebraic mistakes. But, as long as I know the theoretic form of the problem, solving it comes pretty easy. This works as a huge part of the points given per problem.

Example problem:
Assuming an arithmetic sequence has 3rd term of π, and a 6th term of 5π/2.
  • Find the explicit definition of the formula.

Solution

1. Find # of jumps? 6th term - 3rd term = 3 jumps

2. Find the the total difference.

(5π/2) - π =3π/2

3. Now that you have the # of jumps and the total difference. Divide to get the difference per jump.

(3π/2) /(3/1) =π/2

4. No that you have the difference you have to find T1 in order to find th explicit definition.

The 3rd term is π and the difference, so if you subtract the differnce 2/π twice, then you will get the first term.

π - 2(π/2) = 0

5. Given the arithmetic formula. Tn= t1 + (n-1)d

T1= 0

Tn= (n-1)π/2

1 comment:

anto said...

y = mx + b will only work for arithmetic since its the only kind of sequence in which the difference between each term is always the same. Graphically, the difference would be the slope.