Question

Decide whether the given sequence 24, 17, 10, 3, ...... is an A.P.? If yes find its common term (t_n)

Answer 1

The given sequence is 24, 17, 10, 3, ......

Here, t₁ = 24, t₂ = 17, t₃ = 10, t₄ = 3

∴ t₂ – t₁ = 17 – 24 = – 7

t₃ – t₂ = 10 – 17 = – 7

t₄ – t₃ = 3 – 10 = – 7

∴ t₂ – t₁ = t₃ – t₂ = …= – 7 = d = constant

The difference between two consecutive terms is constant.

∴ The given sequence is an A.P.

t_n = a + (n – 1)d

= 24 + (n – 1)(– 7)

= 24 – 7n + 7

= 31 – 7n