Question

Insert five numbers between 11 and 29 such that the resulting sequence is an AP.

Answer 1

To find: Five numbers between 11 and 29, which are in A.P.

Given: (i) The numbers are 11 and 29

Formula used: (i) A_n = a + (n-1)d

Let the five numbers be A₁, A₂, A₃, A₄ and A₅

According to question 11, A₁, A₂, A₃, A₄, A₅ and 29 are in A.P.

We can see that the number of terms in this series is 7

For the above series:-

a = 11, n = 7

A₇ = 29

Using formula, A_n = a + (n-1)d

⇒ A₇ =11 + (7-1)d = 29

⇒ 6d = 29 – 11

⇒ 6d = 18

⇒ d = 3

We can see from the definition that A₁, A₂, A₃, A₄ and A₅ are five arithmetic mean between 11 and 29, where d = 3, a = 11

Therefore, Using formula of arithmetic mean i.e. A_n = a + nd

A₁ = a + nd = 11 + 3 = 14

A₂ = a + nd = 11 + (2)3 = 17

A₃ = a + nd = 11 + (3)3 = 20

A₄ = a + nd = 11 + (4)3 = 23

A₅ = a + nd = 11 + (5)3 = 26

(Ans) 14, 17, 20, 23 and 26 are the required numbers.