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 = `3/4 - 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,

a₅ = a₁ + 4d

= `0 + 4(1/4)`

= 1

a₆ = a₁ + 5d

= `0 + 5(1/4)`

= `5/4`

a₇ = a₁ + 6d

= `0 + 6/4`

= `3/2`