Insert six A.M.s between 15 and −13. - Vidyadip

Question

Insert six A.M.s between $15$ and $−13$.

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Answer

Let $A_1, A_2, A_3, A_4, A_5, A_6,$ be the seven $6$ A.M.s between $15$ and $-13$.
Then, $15 A_1, A_2, A_3, A_4, A_5, A_6, -13$ are in A.P. of $8$ terms
Here,
$-13 = 15 + 7d$
$\Rightarrow d -4$
$= -4$
$A_1 = 15 + d = 15 + (−4) = 11$
$A_2 = 15 + 2d = 15 + (−8) = 7$
$A_3 = 15 + 3d = 15 + (−12) = 3$
$A_4 = 15 + 4d = 15 + (−16) = −1$
$A_5 = 15 + 5d = 15 + (−20) = −5$
$A_6 = 15 + 6d = 15 + (−24) = −9$
The $6$ A.M.S between $15$ and $-13$ are $11, 7, 3, -1, -5$ and $-9$

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