Question

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

`5, 14/3, 13/3, 4,...`

Answer 1

Here,

a₁ = 5

a₂ = `14/3`

a₃ = `13/3`

a₄ = 4

a₂ – a₁ = `14/3 - 5`

= `(14 - 15)/3`

= `(-1)/3`

a₃ – a₂ = `13/3 - 14/3`

= `-1/3`

a₄ – a₃ = `4 - 13/3`

= `(12 - 13)/3`

= `(-1)/3`

Since, difference of successive terms are equal,

Hence `5, 14/3, 13/3, 4,...` is an AP with common difference `-1/3`

Therefore, the next three term will be,

a₅ = a₁ + 4d

= `5 + 4(-1/3)`

= `5 - 4/3`

= `11/3`

a₆ = a₁ + 5d

= `5 + 5(-1/3)`

= `5 - 5/3`

= `10/3`

a₇ = a₁ + 6d

= `5 + 6(-1/3)`

= 5 – 2

= 3