Answer :

Let A_{1}, A_{2}, A_{3}, A_{4}, and A_{5} be five numbers between 8 and 26

such that 8, A_{1}, A_{2}, A_{3}, A_{4}, A_{5}, 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

A_{1} = a + d = 8 + 3 = 11

A_{2} = a + 2d = 8 + 2 × 3 = 8 + 6 = 14

A_{3} = a + 3d = 8 + 3 × 3 = 8 + 9 = 17

A_{4} = a + 4d = 8 + 4 × 3 = 8 + 12 = 20

A_{5} = 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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