Tuesday, May 1, 2007

Prompt Answer

What questions do you have on this topic?
From this topic I’m very doubtful in many things. Most of my questions and doubts are about finding the starting point when given another point in the sequence for example, the problem we made on Monday. Another question I have is how to make an explicit formula.

What mistakes are you most likely to make?
I use to have problems with little details in the problems. Another huge mistake I’ve been making about this topic is that I have been mixing up the different kinds of sequences and using the formulas that aren’t meant to be used.

Example: find the explicit definition of the formula when knowing that the 2nd and 4th terms are 5 and 8.
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1 comment:

anto said...

rrrr Well, to find the first term of a sequence when you are given other terms you just need to follow these simple steps.
1. find r (geometric) or d (arithmetic)
2. find T1

Example:
Given T3 = 6 and T5 = 14, find T1 of this arithmetic series. Here we just need to use the formula for an arithmetic series to solve for d.

Tn = T1 + (n-1)d

In this case Tn = 14, T1 = 6 and n = 3. Solving for d we obtain:

14 = 6 + 2d
d = 4

Now we can solve for T1 using the same formula

Tn = T1 + (n-1)d

Were Tn = either 6 or 14, n = 3 or 5, depending on which Tn you choose, and d = 4

6 = T1 + 8
T1 = -2

Now you can try this harder example:
T5 = 16, T10 = 268912 find T1 of this geometric series

May 6, 2007 at 10:44 AM

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