Let A1, A2, A3, A4, and A5 be five numbers between 8 and 26such that 8, A1, A2, A3, A4, A5, 26 is an A.P.Here, First term = a = 8,Last Term = b = 26,Total no. of terms = n = 7Therefore, 26 = 8 + (7 – 1) d⇒ 6d = 26 – 8 = 18⇒ d = 3A1 = a + d = 8 + 3 = 11A2 = a + 2d = 8 + 2 × 3 = 8 + 6 = 14A3 = a + 3d = 8 + 3 × 3 = 8 + 9 = 17A4 = a + 4d = 8 + 4 × 3 = 8 + 12 = 20A5 = a + 5d = 8 + 5 × 3 = 8 + 15 = 23Thus, the required five numbers between 8 and 26 are 11, 14, 17, 20, and 23.

Q. 144.5( 67 Votes )

Insert five

Class 11th NCERT - Maths 9. Sequences and Series

Answer :

Let A₁, A₂, A₃, A₄, and A₅ be five numbers between 8 and 26

such that 8, A₁, A₂, A₃, A₄, A₅, 26 is an A.P.

Here, First term = a = 8,

Last Term = b = 26,

Total no. of terms = n = 7

Therefore, 26 = 8 + (7 – 1) d

⇒ 6d = 26 – 8 = 18

⇒ d = 3

A₁ = a + d = 8 + 3 = 11

A₂ = a + 2d = 8 + 2 × 3 = 8 + 6 = 14

A₃ = a + 3d = 8 + 3 × 3 = 8 + 9 = 17

A₄ = a + 4d = 8 + 4 × 3 = 8 + 12 = 20

A₅ = a + 5d = 8 + 5 × 3 = 8 + 15 = 23

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

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