document.write( "Question 1146288: For the geometric sequence $\"a\"$ , $\"+ar\"$ , $\"ar%5E2\"$ ... (to infinity), show that the sequence $\"loga\"$ , $\"log%28%28ar%29%29\"$ , $\"log%28%28ar%5E2%29%29\"$ ....(to infinity) is an arithmetic sequence. \n" ); document.write( "

Algebra.Com's Answer #767566 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Two consecutive terms of the given sequence are ar^n and ar^(n+1).

\n" ); document.write( "We need to show that the difference between log(ar^n) and log(ar^(n+1)) is a constant.

\n" ); document.write( " $\"log%28%28ar%5E%28n%2B1%29%29%29-log%28%28ar%5En%29%29\"$ =
\n" ); document.write( "

=
\n" ); document.write( " $\"log%28%28r%29%29\"$

\n" ); document.write( "r is the constant ratio between terms, so log(r) is a constant. \n" ); document.write( "

\n" );