The numbers log (a^3b^7), log(a^5,b^12) and log(a^8,b^15), are the first three terms of an arithmetic sequence, and the the 12th term of the sequence is log(b^n), find the balue of n.
Possible choices of answers.
a) 40
b)56
c)76
d)112
e)143
Hello, Tiger!
Great solution, Grandad!
Here's my approach . . .
The numbers
. . are the first three terms of an arithmetic sequence.
The the 12th term of the sequence is
Find the value of
. .
We have: .
Equate [3] and [2]: .
Substitute into [1]: .
Substitute into [2]: .
The 12th term is: .
We have: .
Therefore: .