Question

Justify whether it is true to say that the following are the nth terms of an AP.

2n – 3

Answer 1

Yes. Here a_n = 2n – 3

Put n = 1, a₁ = 2(1) – 3 = – 1

Put n = 2, a₂ = 2(2) – 3 = 1

Put n = 3, a₃ = 2(3) – 3 = 3

Put n = 4, a₄ = 2(4) – 3 = 5

List of number becomes –1, 1, 3, 5….

Here, a₂ – a₁ = 1 – (-1) = 1 + 1 = 2

a₃ – a₂ = 3 – 1 = 2

a₄ – a₃ = 5 – 3 = 2

∵ a₂ – a₁ = a₃ – a₂ = a₄ – a₃ = …………

Hence, 2n – 3 is the n^th term of an AP.