1.

Show that the sequence `loga ,log((a^2)/b),log((a^3)/(b^2)),log((a^4)/(b^3)), `forms an A.P.

Answer» By symmetry , we find that
` T_(n) = log (a^(n)/(b^(n-1))) and T_(n-1) = log(a^(n-1)/(b^(n-2)))`
` ( T_(n)-T_(n-1)) = log(a^(n)/b^(n -1)))- log( a^(n -1)/b^(n-2))`
` log (a ^(n)/ b^(n-1)xx b^(n-2)/a^(n-1)) = log(a/b)` = constant
Hence, the given sequence in an AP with common differnce ` log(a/b)`


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