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 = -1/3`

a₃ – a₂ = `13/3 - 14/3 = -1/3`

a₄ – a₃ = `4 - 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,

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

`11/3 , 10/3, 3`