Predict the Nth Term in the Sequence

A mathematical model can be made when dealing with a sequence or a series of logarithms. The model should be able to predict the nth term in the sequence and should correctly return its value. Given logab, we can manipulate the variable ‘a’ while keeping b constant, which will produce a pattern.

Mathematical Investigation

Here are some of the basic patterns.

Log­28 =  à  Log­48 =  à Log­88 =  Log­168 =  à Log­328 = à Log­648 = à Log­1288 =

Log­381 = à Log­981 =  à Log­2781 =  à Log­8181 = -à Log­24381 =  à Log­72981 =

Log­525 = à Log­2525 =  à Log­12525 =  à Log­62525 =  à Log­312525 = à Log­1562525 =

Logmmk à Logm2mk à Logm3mk à Logm4mk à Logm5mk à Logm6mk

As you can see, the ‘b’ value remains constant while the ‘a’ value increases exponentially. With this happening, the outcome is pr