Insert five numbers between 8 and 26 such that the resulting sequence

1.	Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
Answer» Let required five numbers be x₁, x₂, x₃, x₄, x₅ ∴ 8, x₁, x₂, x₃, x₄, x₅, 26 are in A.P. ⇒ First term = 8 and seventh term = 26 ⇒ a = 8 and a + 6d - 26 ⇒ 3 = 8 and 6d = 26 – a = 26 – 8 = 18 ⇒ a = 8 and d = 3 Hence x₁= a + d = 8 + 3 = 11 x₂ = a + 2d = 8 + 6 = 14 x₃ = 17, x₄ = 20, x₅ = 23

Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

Answer»

Let required five numbers be x₁, x₂, x₃, x₄, x₅

∴ 8, x₁, x₂, x₃, x₄, x₅, 26 are in A.P.

⇒ First term = 8 and seventh term = 26

⇒ a = 8 and a + 6d - 26

⇒ 3 = 8 and 6d = 26 – a = 26 – 8 = 18

⇒ a = 8 and d = 3

Hence x₁= a + d = 8 + 3 = 11

x₂ = a + 2d = 8 + 6 = 14

x₃ = 17, x₄ = 20, x₅ = 23