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

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- Jan 13th 2010, 05:27 AMTigerSolving for n
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 - Jan 13th 2010, 06:45 AMGrandad
- Jan 13th 2010, 09:00 AMSoroban
Hello, Tiger!

Great solution, Grandad!

Here's my approach . . .

Quote:

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: .