State whether statement in True or False.Two sequences cannot be in bo

1.	State whether statement in True or False.Two sequences cannot be in both A.P. and G.P. together.
Answer» 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

State whether statement in True or False.Two sequences cannot be in both A.P. and G.P. together.

Answer»

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