Insert 6 numbers between 3 and 24 such that the resulting sequenc… - Vidyadip

Question

Insert 6 numbers between 3 and 24 such that the resulting sequence is an A.P.

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Answer

Let A₁, A₂, A₃, A₄, A₅ and A₆ be six numbers between 3 and 24 such that 3, A₁, A₂, A₃, A₄, A5, A₆, 24 are in A.P. Here, a = 3, b = 24, n = 8.
Thus, 24 = 3 + (8 - 1) d, so that d = 3.
Therefore, A1 = a + d = 3 + 3 = 6;
A₂ = a + 2d = 3 + 2 $\times$ 3 = 9;
A₃ = a + 3d = 3 + 3 $\times$ 3 = 12;
A₄ = a + 4d = 3 + 4 $\times$ 3 = 15;
A₅ = a + 5d = 3 + 5 $\times$ 3 = 18;
A₆ = a + 6d = 3 + 6 $\times$ 3 = 21.
Therefore,six numbers between 3 and 24 are 6, 9, 12, 15, 18 and 21.

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