Q30 of 36 Page 161

State whether statement in True or False.

Two sequences cannot be in both A.P. and G.P. together.


Let us consider a sequence in G.P

2, 2, 2 …(i)


If two terms are in AP then,


a2 – a1 = a3 – a2


So, let the sequence (i) is in AP, then


a2 – a1 = 2 – 2 = 0


and a3 – a2 = 2 – 2 = 0


∴ ar – a = ar2 – ar


This means two sequences can be in both A.P and G.P together.


Hence, the given statement is FALSE


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