Question

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

a, 2a + 1, 3a + 2, 4a + 3,...

Answer 1

Here,

a₁ = a

a₂ = 2a + 1

a₃ = 3a + 2

a₄ = 4a + 3

a₂ – a₁ = 2a + 1 – a = a + 1

a₃ – a₂ = 3a + 2 – 2a – 1 = a + 1

a₄ – a₃ = 4a + 3 – 3a – 2 = a + 1

∵ a₂ – a₁ = a₃ – a₂ = a₄ – a₃ = a + 1

Since, difference of successive terms are equal,

Hence, a, 2a + 1, 3a + 2, 4a + 3,… is an AP with common difference a + 1

Therefore, the next three term will be,

a₅ = a + 4d

= a + 4(a + 1)

= 5a + 4

a₆ = a + 5d

= a + 5(a + 1)

= 6a + 5

a₇ = a + 6d

= a + 6(a + 1)

= 7a + 6