Question

show that the sequence log a, log (ab ) , log (ab^2) , log (ab^3) ........ is an A.P . find it's nth term.

Answer 1

For a sequence to be an AP-
if the AP is supposed to be like this..
a, b, c,...
Then-
2b=a+c
in your question
a=logab
b=logab^2
c=logab^3
now
Lhs= 2b= 2 x logab^2 = log (a^2b^4)
according to the property of log
n x loga= loga^n
then Rhs= a +c= log(ab) +log(ab^3) =
log(ab x ab^3)= log (a^2b^4)= Lhs
Due to another logarithmic property
log(a) x log(b) = log(ab)
As Lhs=Rhs
Your Sequence is an AP
Hence Proved..

Answer 2

Answer:

Step-by-step explanation:

a=log a

D= Log(ab)- log a=log(ab/a)=log b

an=a+(n-1)d

an=log a+(n-1)logb

=log(ab^n-1)