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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

\[11, 7, 3, - 1, - 5, - 9\].

  Is there an error in this question or solution?
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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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