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

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Solution

Let the series be $3, a - 5 r, a - 3 r, a - r, a + r, a + 3 r, a + 5 r, 24$

$∴ 3 = a - 7 r, 24 = a + 7 r$
Adding both we get $a = \frac{27}{2}, r = \frac{3}{2}$

$∴$ The numbers are $6, 9, 12, 15, 18, 21$ .

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

Let the series be 3,a−5r,a−3r,a−r,a+r,a+3r,a+5r,24∴3=a−7r,24=a+7rAdding both we get a=272,r=32∴ The numbers are 6,9,12,15,18,21.

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

Let the series be $3, a - 5 r, a - 3 r, a - r, a + r, a + 3 r, a + 5 r, 24$

$∴ 3 = a - 7 r, 24 = a + 7 r$
Adding both we get $a = \frac{27}{2}, r = \frac{3}{2}$

$∴$ The numbers are $6, 9, 12, 15, 18, 21$ .