Question
Find all the sequences which are simultaneously in A.P. and GP.
Solution
Let the sequence 
be in A.P. as well as in G.P.
Let 
be three consecutive terms of an A.P.
∴ 
or 
...(i)
Let r be the common ratio of G.P.
∴ 
and 
and 
in (i), we get
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r = 1∴ 
Hence, all the constant sequences are the only sequences which are in A.P. as well as in G.P.
