Question

Which of the following sequences are A.P.? If they are A.P. find the common difference.

2, `5/2, 3, 7/2,...`

Answer 1

The terms are given:

2, `5/2, 3, 7/2,...`

t₂ − t₁ = `5/2 - 2 = (5 - 4)/2 = 1/2`

t₃ − t₂ = `3 - 5/2 = (6 - 5)/2 = 1/2`

t₄ − t₃ = `7/2 - 3 = (7 - 6)/3 = 1/2`

∵ The difference between two consecutive terms is constant.

Hence, the given sequence is an A.P. and the common difference (d) = constant