# Logarithm Bases Math IA

Logarithmic Sequences IA

Andrew Cherny

Math SL

Scott Learned

1/26/11

In math class, I was given the assignment to evaluate multiple logarithmic sequences to see if any patterns were evident within these sequences.  Using logarithmic rules that I previously learned in math class, I was able to discover multiple patterns within each logarithmic expression.

To begin, I was given the general logarithmic expression:

,…

In order to establish patterns within this general logarithmic expression, I will use multiple examples to help establish a common pattern between all the examples. The first sequence is as followed:

,…

Next, the same logarithmic sequence will be evaluated but more in depth, to try and find a common pattern.

Note: a pattern is already starting to show. While the numerator stays the same throughout the logarithmic sequence, the denominator increases linearly by one. The pattern is also evident within these next two examples of logarithmic sequences.

1)                2)

Cleary, the pattern is noticeable as the sequence goes on. Therefore, I was able to find the  term for each sequence, writing it in the form  where . For the general logarithmic sequence, the  term is the following. …,

That being the case, the nth term for the three examples of logarithmic sequences are the following:         1)

2)

3)

To justify my answer using technology, I used excel to verify that the pattern continues (see appendix 1). By carrying out the pattern to where n=50, I was able to confirm that the ...