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

Question

State whether statement in True or False.

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

Answer 1

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