The 20th term of an arithmetic series is #log20# and the 32nd term is #log32#. Exactly one term in the sequence is a rational number. What is the rational number?

The answer is #1/(n+1)#, but I'm not sure how to get there.

1 Answer
Sep 6, 2016


The tenth term is log10, which equals 1.


If the 20th term is log 20, and the 32nd term is log32, then it follows that the tenth term is log10. Log10=1. 1 is a rational number.

When a log is written without a "base" (the subscript after log), a base of 10 is implied. This is known as the "common log". Log base 10 of 10 equals 1, because 10 to the first power is one. A helpful thing to remember is "the answer to a log is the exponent".

A rational number is a number that can be expressed as a ration, or fraction. Note the word RATIO within RATIOnal. One can be expressed as 1/1.

I don't know where the #1/(n+1)# comes from!