Question

Verify that 5, 14/3, 13/3, 4… is an AP, and then write its next three terms.

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