Question

Verify that the following is an AP, and then write its next three terms.

a + b, (a + 1) + b, (a + 1) + (b + 1),...

Answer 1

Here,

a₁ = a + b

a₂ = (a + 1) + b

a₃ = (a + 1) + (b + 1)

a₂ – a₁ = (a + 1) + b – (a + b)

= a + 1 + b – a – b

= 1

a₃ – a₂ = (a + 1) + (b + 1) – [(a + 1) + b]

= a + 1 + b + 1 – a – 1 – b

= 1

∵ a₂ – a₁ = a₃ – a₂ = 1

Since, difference of successive terms are equal,

Hence, a + b, (a + 1) + b, (a + 1) + (b + 1),... is an AP with common difference 1

Therefore, the next three term will be,

a₄ = a₁ + 3d

= a + b + 3(1)

= (a + 2) + (b + 1)

a₅ = a₁ + 4d

= a + b + 4(1)

= (a + 2) + (b + 2)

a₆ = a₁ + 5d

= a + b + 5(1)

= (a + 3) + (b + 2)