Advanced Math/sequences

Advertisement

Expert: Jack Cheng - 12/5/2006


Question
how do you do this question?
'Consider the geometric sequence t1,t2,t3,t4,... Show that logt1,logt2,logt3,logt4... is an arithmetic sequence

Answer
Hi Carmen,

The answer to this question lies in the logarithm properties that log(a*b) = log(a) + log(b) and log(a^b) = b*log(a).

A geometric seris is one where the next term is derived by multiplying the previous term by a constant r. So t2=r*t1, and t3=r*t2=r*r*r1. The nth term, then, is defined by t1*r^n.

When you take the log of the terms, you get is log(t1*r^n) for the nth term of the sequence. Rewriting that with the log properties, we have:

log(t1*r^n) = log(t1) + log(r^n) = log(t1) + n*log(r)

Why that is an arithmetic sequence, I'll leave to you.

I hope this helps,
Jack

Advanced Math

All Answers

Answers by Expert:

Ask Experts

Volunteer

Jack Cheng

Expertise

I can answer most questions in Math up to single-variable Calculus, including infinite series. I like to think very much, so questions with a lot of twists and turns are highly welcomed! Mathematical questions related to computer science are also highly welcomed! I can also answer some basic questions in discrete mathematics (logics, sets, some algorithms, basic number theory). I am also studying physics (mechanics in particluar), so I am willing to answer some questions relating to it.

Experience

Majoring in Mathematics.

Education/Credentials
I am sophomore/junior status in college working towards bachelor's degrees in Computer Science and Mathematics.

©2012 About.com, a part of The New York Times Company. All rights reserved.