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

Solution:

Let A₁, A₂, A₃, A₄ and A₅ be the five numbers between 8 and 26 such that;

8, A₁, A₂, A₃, A₄, A₅, 26 are in A.P.

Here, a = 8, b = 26, n = 7

Hence,

⇒ 26 = 8 + (7 - 1) d

⇒ 26 = 8 + (6) d

⇒ 6d = 26 - 8

⇒ 6d = 18

⇒ d = 3

Therefore,

A1 = a + d = 8 + 3 = 11

A₂ = a + 2d = 8 + (2)3 = 14

A₃ = a + 3d = 8 + (3)3 = 17

A₄ = a + 4d = 8 + (4)3 = 20

A₅ = a + 5d = 8 + (5)3 = 23

Thus, the required five numbers between 8 and 26 are 11, 14, 17, 20 and 23

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NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.2 Question 14

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

Summary:

The five numbers to be inserted between 8 and 26 such that the resulting sequence is an A.P are 11, 14, 17, 20 and 23