Question

Prove that no matter what is the real number a and b are, the sequence with nth term a + nb is always an A.P. What is the common difference?

Answer 1

Put n = 1

A₁= a + b

Put n = 2

A₂= a + 2b

Put n = 3

A₃= a + 3b

Put n = 4

A₄= a + 4b

Common difference,

d₁ = a₂ – a₁ = a + 2b – a – b = b

Common difference,

d₂= a₃ – a₂ = a+ 3b – a – 2b = b

Common difference,

d₃ = a₄ – a₃ = a+ 4b – a – 3b = b

Since,

d₁ = d₂ = d₃

Therefore, it’s an A.P. with common difference ‘b’