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) = 1

a₃ – a₂ = (a + 1) + (b + 1) – (a + 1) – b = 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,

(a + 1) + (b + 1) + 1, (a + 1) + (b + 1) + 1(2), (a + 1) + (b + 1) + 1(3)

(a + 2) + (b + 1), (a + 2) + (b + 2), (a + 3) + (b + 2)