Question
If An is defined as a geometric sequence, is the sequence 1/An also a geometric sequence? Can someone help explain how I can figure out this statement?
Answers
Steve
For A, the terms are a,ar,ar^2,ar^3,...
For B=1/A, the terms are 1/a, 1/(ar), 1/(ar^2), ...
= (1/a), (1/a)(1/r), (1/a)(1/r)^2, ...
For sequence B, the 1st term is 1/a, and the common ratio is 1/r.
So, it's also a G.P.
For B=1/A, the terms are 1/a, 1/(ar), 1/(ar^2), ...
= (1/a), (1/a)(1/r), (1/a)(1/r)^2, ...
For sequence B, the 1st term is 1/a, and the common ratio is 1/r.
So, it's also a G.P.