Question

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

`0, 1/4, 1/2, 3/4, ...`

Answer 1

Here,

a₁ = 0

a₂ = `1/4`

a₃ =`1/2`

a₄ = `3/4`

a₂ – a₁ = `1/4 - 0 = 1/4`

a₃ – a₂ = `1/2 - 1/4 = 1/4`

a₄ – a₃ = `1/4 - 1/2 = 1/4`

Since, difference of successive terms are equal,

Hence, `0, 1/4, 1/2, 3/4…` is an AP with common difference `1/4`.

Therefore, the next three-term will be,

`3/4 + 1/4 , 3/4 + 2(1/4), 3/4 + 3(1/4)`

`1, 5/4, 3/2`