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# Insert Six A.M.S Between 15 and −13. - Mathematics

Insert six A.M.s between 15 and −13.

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#### Solution

Let $A_1 , A_2 , A_3 , A_4 , A_5 , A_6$ be the 6 A.M.s between 15 and $-$ 13.

Then, 15, $A_1 , A_2 , A_3 , A_4 , A_5 , A_6$  and $-$ 13 are in A.P. whose common difference is as follows:
d = $\frac{- 13 - 15}{6 + 1}$  = $- 4$

$A_1 = 15 + d = 15 + \left( - 4 \right) = 11$

$A_2 = 15 + 2d = 15 + \left( - 8 \right) = 7$

$A_3 = 15 + 3d = 15 + \left( - 12 \right) = 3$

$A_4 = 15 + 4d = 15 + \left( - 16 \right) = - 1$

$A_5 = 15 + 5d = 15 + \left( - 20 \right) = - 5$

$A_6 = 15 + 6d = 15 + \left( - 24 \right) = - 9$

Hence, the required A.M.s are

$11, 7, 3, - 1, - 5, - 9$.

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 19 Arithmetic Progression
Exercise 19.6 | Q 4 | Page 46
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