Question

Which of the following are APs? If they form an A.P. find the common difference d and write three more terms `2, 5/2, 3, 7/2 ....`

Answer 1

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

Here,

a₂ - a₁ = `5/2 - 2 = 1/2`

a₃ - a₂ = `3 - 5/2 = 1/2`

a₄ - a₃ = `7/2 - 3 = 1/2`

⇒ a_n+1 - a_n is same every time.

Therefore, d = 1/2 and the given numbers are in A.P.

Three more terms are

a₅ = `7/2 + 1/2 = 4`

a₆ = `4 + 1/2 = 9/2`

a₇ = `9/2 + 1/2 = 5`